From 5a59b33d5e62f0fce3c567b1ad065ebb81096428 Mon Sep 17 00:00:00 2001
From: Yuichi Motoyama <y-motoyama@issp.u-tokyo.ac.jp>
Date: Sun, 28 Jan 2024 13:34:19 +0900
Subject: [PATCH] coeff of observable

---
 .../file_specification/observable_section.rst | 14 +++
 .../file_specification/observable_section.rst | 24 ++++-
 src/iTPS/load_toml.cpp                        | 27 ++++--
 src/iTPS/main.cpp                             |  7 +-
 src/iTPS/multisite_obs.cpp                    |  2 +-
 src/iTPS/onesite_obs.cpp                      |  8 +-
 src/iTPS/twosite_obs.cpp                      |  4 +-
 src/operator.hpp                              | 33 +++++--
 test/data/AntiferroHeisenberg_real.toml       | 37 +++++++
 .../AntiferroHeisenberg_real.toml             | 54 ++++++++++-
 .../correlation.dat                           | 97 ++++++++++---------
 .../correlation_length.dat                    |  8 +-
 .../density.dat                               | 19 ++--
 .../multisite_obs_4.dat                       | 13 ++-
 .../onesite_obs.dat                           | 33 ++++---
 .../parameters.dat                            |  4 +-
 .../twosite_obs.dat                           | 97 ++++++++++---------
 tool/tenes_std.py                             | 52 ++++++++--
 18 files changed, 370 insertions(+), 163 deletions(-)

diff --git a/docs/sphinx/en/file_specification/observable_section.rst b/docs/sphinx/en/file_specification/observable_section.rst
index f64b8129..6e27ad76 100644
--- a/docs/sphinx/en/file_specification/observable_section.rst
+++ b/docs/sphinx/en/file_specification/observable_section.rst
@@ -18,6 +18,8 @@ Define one-body operators that indicate physical quantities defined at each site
    ``sites``,    "Site number",         Integer or a list of integer
    ``dim``,      "Dimension of an operator",       Integer
    ``elements``, "Non-zero elements of an operator", String
+   ``coeff``,    "Coefficient of operator (real part)", Float
+   ``coeff_im``,  "Coefficient of operator (imaginary part)", Float
 
 ``name``  specifies an operator name.
 
@@ -35,6 +37,9 @@ One element is specified by one line consisting of two integers and two floating
 - The first two integers are the state numbers before and after the act of the operator, respectively.
 - The latter two floats indicate the real and imaginary parts of the elements of the operator, respectively.
 
+``coeff`` and ``coeff_im`` are real and imaginary parts of the coefficient of the operator, respectively.
+If omitted, they are set to 1.0 and 0.0, respectively.
+
 Example
 .......
 
@@ -93,6 +98,8 @@ Define two-body operators that indicate physical quantities defined on two sites
    ``dim``,      "Dimension of an operator",           Integer
    ``elements``, "Non-zero elements of an operator",   String
    ``ops``,      "Index of onesite operators",         A list of integer
+   ``coeff``,    "Coefficient of operator (real part)", Float
+   ``coeff_im``,  "Coefficient of operator (imaginary part)", Float
 
 
 ``name``  specifies an operator name.
@@ -123,6 +130,9 @@ For example, if :math:`S^z` is defined as ``group = 0`` in ``observable.onesite`
 
 If both ``elements`` and ``ops`` are defined, the process will end in error.
 
+``coeff`` and ``coeff_im`` are real and imaginary parts of the coefficient of the operator, respectively.
+If omitted, they are set to 1.0 and 0.0, respectively.
+
 Example
 .......
 
@@ -193,6 +203,8 @@ It is defined as a direct product of one-body operators defined in ``observable.
    ``group``,      "Identification number of operators", Integer
    ``multisites``, "Sites",                              String
    ``ops``,        "Index of onesite operators",         List of integers
+   ``coeff``,      "Coefficient of operator (real part)", Float
+   ``coeff_im``,    "Coefficient of operator (imaginary part)", Float
 
 ``name``  specifies an operator name.
 
@@ -210,3 +222,5 @@ One line consisting of integers means a set sites.
 Using ``ops``, a multi-body operator can be defined as a direct product of the one-body operators defined in ``observable.onesite``.
 For example, if :math:`S^z` is defined as ``group = 0`` in ``observable.onesite``,  :math:`S^z_i S^z_j S^z_k` can be expressed as ``ops = [0,0,0]``.
 
+``coeff`` and ``coeff_im`` are real and imaginary parts of the coefficient of the operator, respectively.
+If omitted, they are set to 1.0 and 0.0, respectively.
diff --git a/docs/sphinx/ja/file_specification/observable_section.rst b/docs/sphinx/ja/file_specification/observable_section.rst
index ca1ffc61..5ea71226 100644
--- a/docs/sphinx/ja/file_specification/observable_section.rst
+++ b/docs/sphinx/ja/file_specification/observable_section.rst
@@ -14,11 +14,13 @@
    :header: "名前", "説明", "型"
    :widths: 15, 30, 20
 
-   ``name``,     "演算子の名前",       文字列
-   ``group``,    "演算子の識別番号",   整数
-   ``sites``,    "サイト番号",         整数 or 整数のリスト
-   ``dim``,      "演算子の次元",       整数
-   ``elements``, "演算子の非ゼロ要素", 文字列
+   ``name``,     "演算子の名前",               文字列
+   ``group``,    "演算子の識別番号",           整数
+   ``sites``,    "サイト番号",                 整数 or 整数のリスト
+   ``dim``,      "演算子の次元",               整数
+   ``elements``, "演算子の非ゼロ要素",         文字列
+   ``coeff``,    "演算子にかかる係数（実部）", 実数
+   ``coeff_im``, "演算子にかかる係数（虚部）", 実数
 
 ``name`` は演算子の名前です。
 
@@ -36,6 +38,9 @@
 - 最初の2つはそれぞれ演算子が作用する前と後の状態番号を示します。
 - あとの2つはそれぞれ演算子の要素の実部と虚部を示します。
 
+``coeff``, ``coeff_im`` は演算子にかかる係数の実部と虚部です。
+省略した場合はそれぞれ 1.0, 0.0 になります。
+
 例
 ....
 
@@ -95,6 +100,8 @@ S=1/2 のSz 演算子
    ``dim``,      "演算子の次元",             整数のリスト
    ``elements``, "演算子の非ゼロ要素",       文字列
    ``ops``,      "onesite 演算子の識別番号", 整数のリスト
+   ``coeff``,    "演算子にかかる係数（実部）", 実数
+   ``coeff_im``, "演算子にかかる係数（虚部）", 実数
 
 ``name`` は演算子の名前です。
 
@@ -124,6 +131,9 @@ S=1/2 のSz 演算子
 
 ``elements`` と ``ops`` を同時に定義した場合にはエラー終了します。
 
+``coeff``, ``coeff_im`` は演算子にかかる係数の実部と虚部です。
+省略した場合はそれぞれ 1.0, 0.0 になります。
+
 例
 ....
 ここでは具体例として、``Lsub=[2,2]`` の正方格子 S=1/2 ハイゼンベルグ模型のボンドハミルトニアンのエネルギーを求めるため、
@@ -197,6 +207,8 @@ S=1/2 のSz 演算子
    ``group``,      "演算子の識別番号",         整数
    ``multisites``, "サイトの組み合わせ",       文字列
    ``ops``,        "onesite 演算子の識別番号", 整数のリスト
+   ``coeff``,    "演算子にかかる係数（実部）", 実数
+   ``coeff_im``, "演算子にかかる係数（虚部）", 実数
 
 ``name`` は演算子の名前です。
 
@@ -215,3 +227,5 @@ S=1/2 のSz 演算子
 例えば ``observable.onesite`` の ``group=0`` として :math:`S^z` を定義していた場合には、
 ``ops = [0,0,0]`` として :math:`S^z_iS^z_jS^z_k` を表現できます。
 
+``coeff``, ``coeff_im`` は演算子にかかる係数の実部と虚部です。
+省略した場合はそれぞれ 1.0, 0.0 になります。
diff --git a/src/iTPS/load_toml.cpp b/src/iTPS/load_toml.cpp
index 91f4ae97..c9cef62c 100644
--- a/src/iTPS/load_toml.cpp
+++ b/src/iTPS/load_toml.cpp
@@ -78,6 +78,13 @@ struct bittype<long long int> {
   typedef int64_t type;
 };
 
+template <class T>
+T reduce(double re, double im);
+template <>
+std::complex<double> reduce<std::complex<double>>(double re, double im) { return std::complex<double>(re, im); }
+template <>
+double reduce<double>(double re, double im) { return re; }
+
 }  // end of namespace detail
 
 template <class T>
@@ -516,9 +523,17 @@ Operators<tensor> load_operator(decltype(cpptoml::parse_file("")) param,
 
   auto group = find<int>(param, "group");
   auto name = find_or(param, "name", std::string(""));
+  auto coeff_re = find_or(param, "coeff", 1.0);
+  auto coeff_im = find_or(param, "coeff_im", 0.0);
+  typename tensor::value_type coeff = detail::reduce<typename tensor::value_type>(coeff_re, coeff_im);
+  auto is_real = std::is_same<typename tensor::value_type, double>::value;
+  if(is_real && coeff_im != 0.0){
+    std::stringstream ss;
+    ss << "parameter.general.is_real is true but coeff_im is not zero in a section " << tablename;
+    throw tenes::input_error(ss.str());
+  }
 
   std::vector<Operator<tensor>> ret;
-
   if (nbody == 1) {
     auto site_int = param->get_as<int>("sites");
     auto site_arr = param->get_array_of<int64_t>("sites");
@@ -536,7 +551,7 @@ Operators<tensor> load_operator(decltype(cpptoml::parse_file("")) param,
       throw input_error(detail::msg_cannot_find("sites", tablename));
     }
     for (int s : sites) {
-      ret.emplace_back(name, group, s, A);
+      ret.emplace_back(name, group, s, A, coeff);
     }
   } else if (nbody == 2) {
     auto bonds_str = find<std::string>(param, "bonds");
@@ -544,10 +559,10 @@ Operators<tensor> load_operator(decltype(cpptoml::parse_file("")) param,
     for (auto bond : bonds) {
       if (elements) {
         ret.emplace_back(name, group, std::get<0>(bond), std::get<1>(bond),
-                         std::get<2>(bond), A);
+                         std::get<2>(bond), A, coeff);
       } else {
         ret.emplace_back(name, group, std::get<0>(bond), std::get<1>(bond),
-                         std::get<2>(bond), op_ind);
+                         std::get<2>(bond), op_ind, coeff);
       }
     }
   } else {
@@ -556,10 +571,10 @@ Operators<tensor> load_operator(decltype(cpptoml::parse_file("")) param,
     for (auto ms : mss) {
       if (elements) {
         ret.emplace_back(name, group, std::get<0>(ms), std::get<1>(ms),
-                         std::get<2>(ms), A);
+                         std::get<2>(ms), A, coeff);
       } else {
         ret.emplace_back(name, group, std::get<0>(ms), std::get<1>(ms),
-                         std::get<2>(ms), op_ind);
+                         std::get<2>(ms), op_ind, coeff);
       }
     }
   }
diff --git a/src/iTPS/main.cpp b/src/iTPS/main.cpp
index 20f6c82e..4e7c409c 100644
--- a/src/iTPS/main.cpp
+++ b/src/iTPS/main.cpp
@@ -48,23 +48,24 @@ tenes::Operators<mptensor::Tensor<tenes::mptensor_matrix_type, double>> to_real(
   }
   MPI_Comm comm = ops[0].op.get_comm();
   for (auto const& op : ops) {
+    double coeff = std::real(op.coeff);
     if (op.is_onesite()) {
       mptensor::Tensor<tenes::mptensor_matrix_type, double> A(comm,
                                                               op.op.shape());
       for (size_t lindex = 0; lindex < op.op.local_size(); ++lindex) {
         A[lindex] = op.op[lindex].real();
       }
-      ret.emplace_back(op.name, op.group, op.source_site, A);
+      ret.emplace_back(op.name, op.group, op.source_site, A, coeff);
     } else if (op.ops_indices.empty()) {
       mptensor::Tensor<tenes::mptensor_matrix_type, double> A(comm,
                                                               op.op.shape());
       for (size_t lindex = 0; lindex < op.op.local_size(); ++lindex) {
         A[lindex] = op.op[lindex].real();
       }
-      ret.emplace_back(op.name, op.group, op.source_site, op.dx, op.dy, A);
+      ret.emplace_back(op.name, op.group, op.source_site, op.dx, op.dy, A, coeff);
     } else {
       ret.emplace_back(op.name, op.group, op.source_site, op.dx, op.dy,
-                       op.ops_indices);
+                       op.ops_indices, coeff);
     }
   }
   return ret;
diff --git a/src/iTPS/multisite_obs.cpp b/src/iTPS/multisite_obs.cpp
index cacb8f02..54819856 100644
--- a/src/iTPS/multisite_obs.cpp
+++ b/src/iTPS/multisite_obs.cpp
@@ -202,7 +202,7 @@ auto iTPS<ptensor>::measure_multisite()
           core::Contract(C_, eTt_, eTr_, eTb_, eTl_, Tn_, op_, is_density, is_meanfield);
       value += localvalue;
     }
-    ret[op.group][{op.source_site, op.dx, op.dy}] = value / norm;
+    ret[op.group][{op.source_site, op.dx, op.dy}] = op.coeff * value / norm;
   }
   // ret.push_back(norms);
 
diff --git a/src/iTPS/onesite_obs.cpp b/src/iTPS/onesite_obs.cpp
index be395e9c..a5b442db 100644
--- a/src/iTPS/onesite_obs.cpp
+++ b/src/iTPS/onesite_obs.cpp
@@ -66,7 +66,7 @@ auto iTPS<tensor>::measure_onesite()
     for (auto const &op : onesite_operators) {
       const int i = op.source_site;
       const auto val = core::Contract_one_site_iTPS_MF(Tn_[i], op.op);
-      local_obs[op.group][i] = val / norm[i];
+      local_obs[op.group][i] = op.coeff * val / norm[i];
     }
   } else {  // CTM
     if (is_density) {
@@ -80,7 +80,7 @@ auto iTPS<tensor>::measure_onesite()
         const auto val = core::Contract_one_site_density_CTM(
             C1[i], C2[i], C3[i], C4[i], eTt[i], eTr[i], eTb[i], eTl[i], Tn[i],
             op.op);
-        local_obs[op.group][i] = val / norm[i];
+        local_obs[op.group][i] = op.coeff * val / norm[i];
       }
     } else {
       for (int i = 0; i < N_UNIT; ++i) {
@@ -93,7 +93,7 @@ auto iTPS<tensor>::measure_onesite()
         const auto val = core::Contract_one_site_iTPS_CTM(
             C1[i], C2[i], C3[i], C4[i], eTt[i], eTr[i], eTb[i], eTl[i], Tn[i],
             op.op);
-        local_obs[op.group][i] = val / norm[i];
+        local_obs[op.group][i] = op.coeff * val / norm[i];
       }
     }
   }
@@ -240,7 +240,7 @@ auto iTPS<tensor>::measure_onesite_density()
     const auto val = core::Contract_one_site_density_CTM(
         C1[i], C2[i], C3[i], C4[i], eTt[i], eTr[i], eTb[i], eTl[i], Tn[i],
         op.op);
-    local_obs[op.group][i] = val / norm[i];
+    local_obs[op.group][i] = op.coeff * val / norm[i];
   }
   //  }
   double norm_real_min = 1e100;
diff --git a/src/iTPS/twosite_obs.cpp b/src/iTPS/twosite_obs.cpp
index 6fd5279f..4c7625d1 100644
--- a/src/iTPS/twosite_obs.cpp
+++ b/src/iTPS/twosite_obs.cpp
@@ -258,7 +258,7 @@ auto iTPS<ptensor>::measure_twosite()
       //         : core::Contract_CTM(C_, eTt_, eTr_, eTb_, eTl_, Tn_, op_);
       value += localvalue;
     }
-    ret[op.group][{op.source_site, op.dx[0], op.dy[0]}] = value / norm;
+    ret[op.group][{op.source_site, op.dx[0], op.dy[0]}] = op.coeff * value / norm;
   }
   ret.push_back(norms);
 
@@ -583,7 +583,7 @@ auto iTPS<ptensor>::measure_twosite_density()
         }
       }
     }
-    ret[op.group][{op.source_site, op.dx[0], op.dy[0]}] = value / norm;
+    ret[op.group][{op.source_site, op.dx[0], op.dy[0]}] = op.coeff * value / norm;
   }
   ret.push_back(norms);
 
diff --git a/src/operator.hpp b/src/operator.hpp
index 5ba78909..f67df65a 100644
--- a/src/operator.hpp
+++ b/src/operator.hpp
@@ -19,11 +19,14 @@
 
 #include <vector>
 #include <string>
+#include <iostream>
 
 namespace tenes {
 
 template <class tensor>
 struct Operator {
+  using value_type = typename tensor::value_type;
+
   std::string name;
   int group;
   int source_site;
@@ -31,6 +34,7 @@ struct Operator {
   std::vector<int> dy;
   tensor op;
   std::vector<int> ops_indices;
+  typename tensor::value_type coeff;
 
   /*!
    * @brief Constructor for a one-site operator.
@@ -39,9 +43,10 @@ struct Operator {
    * @param[in] group Group of the operator.
    * @param[in] site Site of the operator.
    * @param[in] op Operator tensor.
+   * @param[in] coeff coefficient of operator (default: 1.0).
    */
-  Operator(std::string const &name, int group, int site, tensor const &op)
-      : name(name), group(group), source_site(site), dx(0), dy(0), op(op) {
+  Operator(std::string const &name, int group, int site, tensor const &op, value_type coeff=static_cast<value_type>(1.0))
+      : name(name), group(group), source_site(site), dx(0), dy(0), op(op), coeff(coeff) {
     if (op.rank() != 2) {
       throw std::runtime_error("Operator tensor must be rank 2.");
     }
@@ -56,15 +61,17 @@ struct Operator {
    * @param[in] dx X displacement of the other site.
    * @param[in] dy Y displacement of the other site.
    * @param[in] op Operator tensor.
+   * @param[in] coeff coefficient of operator (default: 1.0).
    */
   Operator(std::string const &name, int group, int source_site, int dx, int dy,
-           tensor const &op)
+           tensor const &op, value_type coeff=static_cast<value_type>(1.0))
       : name(name),
         group(group),
         source_site(source_site),
         dx(1, dx),
         dy(1, dy),
-        op(op) {
+        op(op),
+        coeff(coeff) {
     if (op.rank() != 4) {
       throw std::runtime_error("Operator tensor must be rank 4.");
     }
@@ -80,15 +87,17 @@ struct Operator {
    * @param[in] dx X displacement of the other site.
    * @param[in] dy Y displacement of the other site.
    * @param[in] ops_indices Onesite operator indices.
+   * @param[in] coeff coefficient of operator (default: 1.0).
    */
   Operator(std::string const &name, int group, int source_site, int dx, int dy,
-           std::vector<int> const &ops_indices)
+           std::vector<int> const &ops_indices, value_type coeff=static_cast<value_type>(1.0))
       : name(name),
         group(group),
         source_site(source_site),
         dx(1, dx),
         dy(1, dy),
-        ops_indices(ops_indices) {
+        ops_indices(ops_indices),
+        coeff(coeff){
     if (ops_indices.size() != 2) {
       throw std::runtime_error(
           "Operator must be a product of two one-site operators.");
@@ -104,16 +113,18 @@ struct Operator {
    * @param[in] dx X displacement of the other sites.
    * @param[in] dy Y displacement of the other sites.
    * @param[in] op Operator tensor.
+   * @param[in] coeff coefficient of operator (default: 1.0).
    */
   Operator(std::string const &name, int group, int source_site,
            std::vector<int> const &dx, std::vector<int> const &dy,
-           tensor const &op)
+           tensor const &op, value_type coeff=static_cast<value_type>(1.0))
       : name(name),
         group(group),
         source_site(source_site),
         dx(dx),
         dy(dy),
-        op(op) {
+        op(op),
+        coeff(coeff) {
     if (dx.size() != dy.size()) {
       throw std::runtime_error("dx and dy must have the same size.");
     }
@@ -132,16 +143,18 @@ struct Operator {
    * @param[in] dx X displacement of the other sites.
    * @param[in] dy Y displacement of the other sites.
    * @param[in] ops_indices Onesite operator indices.
+   * @param[in] coeff coefficient of operator (default: 1.0).
    */
   Operator(std::string const &name, int group, int source_site,
            std::vector<int> const &dx, std::vector<int> const &dy,
-           std::vector<int> const &ops_indices)
+           std::vector<int> const &ops_indices, value_type coeff=static_cast<value_type>(1.0))
       : name(name),
         group(group),
         source_site(source_site),
         dx(dx),
         dy(dy),
-        ops_indices(ops_indices) {
+        ops_indices(ops_indices),
+        coeff(coeff) {
     if (dx.size() != dy.size()) {
       throw std::runtime_error("dx and dy must have the same size.");
     }
diff --git a/test/data/AntiferroHeisenberg_real.toml b/test/data/AntiferroHeisenberg_real.toml
index 614a54a6..2bf19c6f 100644
--- a/test/data/AntiferroHeisenberg_real.toml
+++ b/test/data/AntiferroHeisenberg_real.toml
@@ -44,6 +44,16 @@ elements = """
 1 0  0.5 0.0
 0 1  0.5 0.0
 """
+[[observable.onesite]]
+name = "2Sz"
+group = 2
+sites = []
+dim = 2
+elements = """
+0 0  0.5 0.0
+1 1  -0.5 0.0
+"""
+coeff = 2.0
 
 [[observable.twosite]]
 name = "bond_hamiltonian"
@@ -115,6 +125,21 @@ elements = """
 1 0 0 1  0.25 0.0
 0 0 1 1  -0.25 0.0
 """
+[[observable.twosite]]
+name = "2SzSz"
+group = 4
+bonds = """
+0 1 0
+1 1 0
+2 1 0
+3 1 0
+0 0 1
+1 0 1
+2 0 1
+3 0 1
+"""
+ops = [0, 0]
+coeff = 2.0
 
 [[observable.multisite]]
 name = "SzSzSzSz"
@@ -127,6 +152,18 @@ multisites = """
 """
 ops = [0,0,0,0]
 
+[[observable.multisite]]
+name = "2SzSzSzSz"
+group = 1
+multisites = """
+0 1 0 1 1 0 1
+1 1 0 1 1 0 1
+2 1 0 1 1 0 1
+3 1 0 1 1 0 1
+"""
+ops = [0,0,0,0]
+coeff = 2.0
+
 [evolution]
 [[evolution.simple]]
 source_site = 0
diff --git a/test/data/output_AntiferroHeisenberg_real/AntiferroHeisenberg_real.toml b/test/data/output_AntiferroHeisenberg_real/AntiferroHeisenberg_real.toml
index 658a50db..2bf19c6f 100644
--- a/test/data/output_AntiferroHeisenberg_real/AntiferroHeisenberg_real.toml
+++ b/test/data/output_AntiferroHeisenberg_real/AntiferroHeisenberg_real.toml
@@ -21,6 +21,10 @@ virtual_dim = [2, 2, 2, 2]
 initial_state = [0.0]
 noise = 0.01
 
+[correlation]
+r_max = 3
+operators = [[0,0], [0,1]]
+
 [observable]
 [[observable.onesite]]
 name = "Sz"
@@ -40,9 +44,19 @@ elements = """
 1 0  0.5 0.0
 0 1  0.5 0.0
 """
+[[observable.onesite]]
+name = "2Sz"
+group = 2
+sites = []
+dim = 2
+elements = """
+0 0  0.5 0.0
+1 1  -0.5 0.0
+"""
+coeff = 2.0
 
 [[observable.twosite]]
-name = "hamiltonian"
+name = "bond_hamiltonian"
 group = 0
 bonds = """
 0 1 0
@@ -111,6 +125,44 @@ elements = """
 1 0 0 1  0.25 0.0
 0 0 1 1  -0.25 0.0
 """
+[[observable.twosite]]
+name = "2SzSz"
+group = 4
+bonds = """
+0 1 0
+1 1 0
+2 1 0
+3 1 0
+0 0 1
+1 0 1
+2 0 1
+3 0 1
+"""
+ops = [0, 0]
+coeff = 2.0
+
+[[observable.multisite]]
+name = "SzSzSzSz"
+group = 0
+multisites = """
+0 1 0 1 1 0 1
+1 1 0 1 1 0 1
+2 1 0 1 1 0 1
+3 1 0 1 1 0 1
+"""
+ops = [0,0,0,0]
+
+[[observable.multisite]]
+name = "2SzSzSzSz"
+group = 1
+multisites = """
+0 1 0 1 1 0 1
+1 1 0 1 1 0 1
+2 1 0 1 1 0 1
+3 1 0 1 1 0 1
+"""
+ops = [0,0,0,0]
+coeff = 2.0
 
 [evolution]
 [[evolution.simple]]
diff --git a/test/data/output_AntiferroHeisenberg_real/correlation.dat b/test/data/output_AntiferroHeisenberg_real/correlation.dat
index 558b18e2..cac72c45 100644
--- a/test/data/output_AntiferroHeisenberg_real/correlation.dat
+++ b/test/data/output_AntiferroHeisenberg_real/correlation.dat
@@ -9,52 +9,53 @@
 # The names of operators are the following: 
 # 0: Sz              
 # 1: Sx              
+# 2: 2Sz             
 
-0 0 0 1 0 -1.61814083059261232e-01 0.00000000000000000e+00 
-0 0 1 1 0 -7.69262211008062136e-02 0.00000000000000000e+00 
-0 0 0 2 0 1.51101865176695660e-01 0.00000000000000000e+00 
-0 0 1 2 0 -7.68731988366160718e-02 0.00000000000000000e+00 
-0 0 0 3 0 -1.49061437639722988e-01 0.00000000000000000e+00 
-0 0 1 3 0 -4.86911672846061377e-02 0.00000000000000000e+00 
-0 0 0 0 1 -1.33324968627196561e-01 0.00000000000000000e+00 
-0 0 1 0 1 -1.09228626247116448e-01 0.00000000000000000e+00 
-0 0 0 0 2 1.47921448594502625e-01 0.00000000000000000e+00 
-0 0 1 0 2 -7.70665086768835550e-02 0.00000000000000000e+00 
-0 0 0 0 3 -1.32305314089022769e-01 0.00000000000000000e+00 
-0 0 1 0 3 -9.14168175696279950e-02 0.00000000000000000e+00 
-0 1 0 1 0 -1.62023966039102713e-01 0.00000000000000000e+00 
-0 1 1 1 0 9.83353666819980904e-02 0.00000000000000000e+00 
-0 1 0 2 0 1.52489835935105650e-01 0.00000000000000000e+00 
-0 1 1 2 0 4.65300818653293785e-02 0.00000000000000000e+00 
-0 1 0 3 0 -1.49056944997098123e-01 0.00000000000000000e+00 
-0 1 1 3 0 7.95224809542846023e-02 0.00000000000000000e+00 
-0 1 0 0 1 -1.71118008938635602e-01 0.00000000000000000e+00 
-0 1 1 0 1 -2.45303989785474498e-02 0.00000000000000000e+00 
-0 1 0 0 2 1.52001220434321266e-01 0.00000000000000000e+00 
-0 1 1 0 2 4.68802665173839034e-02 0.00000000000000000e+00 
-0 1 0 0 3 -1.46855044813913649e-01 0.00000000000000000e+00 
-0 1 1 0 3 -3.79097815452288656e-02 0.00000000000000000e+00 
-0 2 0 1 0 -1.65776212997030048e-01 0.00000000000000000e+00 
-0 2 1 1 0 -2.85894408258394270e-03 0.00000000000000000e+00 
-0 2 0 2 0 1.26142514742576900e-01 0.00000000000000000e+00 
-0 2 1 2 0 7.72324683987457572e-02 0.00000000000000000e+00 
-0 2 0 3 0 -1.30780421583722717e-01 0.00000000000000000e+00 
-0 2 1 3 0 -3.26773769543835246e-02 0.00000000000000000e+00 
-0 2 0 0 1 -1.33365169593476440e-01 0.00000000000000000e+00 
-0 2 1 0 1 8.92440518635981700e-02 0.00000000000000000e+00 
-0 2 0 0 2 1.20436413956494903e-01 0.00000000000000000e+00 
-0 2 1 0 2 8.10044814931354384e-02 0.00000000000000000e+00 
-0 2 0 0 3 -1.32303915371563996e-01 0.00000000000000000e+00 
-0 2 1 0 3 7.07780020062377252e-02 0.00000000000000000e+00 
-0 3 0 1 0 -1.66391777687540071e-01 0.00000000000000000e+00 
-0 3 1 1 0 -8.14152807029617093e-02 0.00000000000000000e+00 
-0 3 0 2 0 1.44059463516688607e-01 0.00000000000000000e+00 
-0 3 1 2 0 3.18357113679693451e-02 0.00000000000000000e+00 
-0 3 0 3 0 -1.30790812987773120e-01 0.00000000000000000e+00 
-0 3 1 3 0 -8.95361260748531312e-02 0.00000000000000000e+00 
-0 3 0 0 1 -1.71537906054281014e-01 0.00000000000000000e+00 
-0 3 1 0 1 -3.54238944218439461e-02 0.00000000000000000e+00 
-0 3 0 0 2 1.43331346702437440e-01 0.00000000000000000e+00 
-0 3 1 0 2 3.32403019967970059e-02 0.00000000000000000e+00 
-0 3 0 0 3 -1.46856745636973290e-01 0.00000000000000000e+00 
-0 3 1 0 3 -4.73152954282259133e-02 0.00000000000000000e+00 
+0 0 0 1 0 -1.61814083059259678e-01 0.00000000000000000e+00 
+0 0 1 1 0 -7.69262211008061580e-02 0.00000000000000000e+00 
+0 0 0 2 0 1.51101865176693384e-01 0.00000000000000000e+00 
+0 0 1 2 0 -7.68731988366181673e-02 0.00000000000000000e+00 
+0 0 0 3 0 -1.49061437639721545e-01 0.00000000000000000e+00 
+0 0 1 3 0 -4.86911672846055896e-02 0.00000000000000000e+00 
+0 0 0 0 1 -1.33324968627193369e-01 0.00000000000000000e+00 
+0 0 1 0 1 -1.09228626247116767e-01 0.00000000000000000e+00 
+0 0 0 0 2 1.47921448594500127e-01 0.00000000000000000e+00 
+0 0 1 0 2 -7.70665086768852758e-02 0.00000000000000000e+00 
+0 0 0 0 3 -1.32305314089019938e-01 0.00000000000000000e+00 
+0 0 1 0 3 -9.14168175696282170e-02 0.00000000000000000e+00 
+0 1 0 1 0 -1.62023966039100908e-01 0.00000000000000000e+00 
+0 1 1 1 0 9.83353666819996586e-02 0.00000000000000000e+00 
+0 1 0 2 0 1.52489835935104817e-01 0.00000000000000000e+00 
+0 1 1 2 0 4.65300818653292397e-02 0.00000000000000000e+00 
+0 1 0 3 0 -1.49056944997096569e-01 0.00000000000000000e+00 
+0 1 1 3 0 7.95224809542867533e-02 0.00000000000000000e+00 
+0 1 0 0 1 -1.71118008938634658e-01 0.00000000000000000e+00 
+0 1 1 0 1 -2.45303989785445077e-02 0.00000000000000000e+00 
+0 1 0 0 2 1.52001220434320433e-01 0.00000000000000000e+00 
+0 1 1 0 2 4.68802665173836675e-02 0.00000000000000000e+00 
+0 1 0 0 3 -1.46855044813912455e-01 0.00000000000000000e+00 
+0 1 1 0 3 -3.79097815452261108e-02 0.00000000000000000e+00 
+0 2 0 1 0 -1.65776212997028355e-01 0.00000000000000000e+00 
+0 2 1 1 0 -2.85894408258031843e-03 0.00000000000000000e+00 
+0 2 0 2 0 1.26142514742574346e-01 0.00000000000000000e+00 
+0 2 1 2 0 7.72324683987454935e-02 0.00000000000000000e+00 
+0 2 0 3 0 -1.30780421583720247e-01 0.00000000000000000e+00 
+0 2 1 3 0 -3.26773769543806450e-02 0.00000000000000000e+00 
+0 2 0 0 1 -1.33365169593473304e-01 0.00000000000000000e+00 
+0 2 1 0 1 8.92440518635987251e-02 0.00000000000000000e+00 
+0 2 0 0 2 1.20436413956491697e-01 0.00000000000000000e+00 
+0 2 1 0 2 8.10044814931352858e-02 0.00000000000000000e+00 
+0 2 0 0 3 -1.32303915371561137e-01 0.00000000000000000e+00 
+0 2 1 0 3 7.07780020062389048e-02 0.00000000000000000e+00 
+0 3 0 1 0 -1.66391777687538850e-01 0.00000000000000000e+00 
+0 3 1 1 0 -8.14152807029630693e-02 0.00000000000000000e+00 
+0 3 0 2 0 1.44059463516686886e-01 0.00000000000000000e+00 
+0 3 1 2 0 3.18357113679664239e-02 0.00000000000000000e+00 
+0 3 0 3 0 -1.30790812987770622e-01 0.00000000000000000e+00 
+0 3 1 3 0 -8.95361260748535476e-02 0.00000000000000000e+00 
+0 3 0 0 1 -1.71537906054279793e-01 0.00000000000000000e+00 
+0 3 1 0 1 -3.54238944218441265e-02 0.00000000000000000e+00 
+0 3 0 0 2 1.43331346702435913e-01 0.00000000000000000e+00 
+0 3 1 0 2 3.32403019967941263e-02 0.00000000000000000e+00 
+0 3 0 0 3 -1.46856745636971792e-01 0.00000000000000000e+00 
+0 3 1 0 3 -4.73152954282254692e-02 0.00000000000000000e+00 
diff --git a/test/data/output_AntiferroHeisenberg_real/correlation_length.dat b/test/data/output_AntiferroHeisenberg_real/correlation_length.dat
index dad3699e..5206f280 100644
--- a/test/data/output_AntiferroHeisenberg_real/correlation_length.dat
+++ b/test/data/output_AntiferroHeisenberg_real/correlation_length.dat
@@ -5,7 +5,7 @@
 # $4-: eigenvalues e_i = -log|t_i/t_0|
 #      where i > 0 and t_i is i-th largest eigenvalue of T
 
-0 0 8.44994724744467240e-01 1.18343934076323087e+00 1.31217387840878708e+00 1.50088448589389079e+00
-0 1 8.45007547885713084e-01 1.18342138185876844e+00 1.31207991892442499e+00 1.49884260767436839e+00
-1 0 7.09058133674783431e-01 1.41032159777559229e+00 1.57230304927109032e+00 1.80264278143236978e+00
-1 1 7.09013376311946608e-01 1.41041062610365642e+00 1.57276526937484551e+00 1.80524017948036231e+00
+0 0 8.44994724744483339e-01 1.18343934076320823e+00 1.31217387840875177e+00 1.50088448589384638e+00
+0 1 8.45007547885718746e-01 1.18342138185876045e+00 1.31207991892443365e+00 1.49884260767438549e+00
+1 0 7.09058133674792535e-01 1.41032159777557409e+00 1.57230304927106412e+00 1.80264278143232781e+00
+1 1 7.09013376311950050e-01 1.41041062610364953e+00 1.57276526937485217e+00 1.80524017948038074e+00
diff --git a/test/data/output_AntiferroHeisenberg_real/density.dat b/test/data/output_AntiferroHeisenberg_real/density.dat
index bb99b257..aa2cde5d 100644
--- a/test/data/output_AntiferroHeisenberg_real/density.dat
+++ b/test/data/output_AntiferroHeisenberg_real/density.dat
@@ -1,8 +1,11 @@
-Energy           = -5.43694699199371301e-01  0.00000000000000000e+00
-Sz               =  6.11534505262875672e-03  0.00000000000000000e+00
-Sx               = -1.18113776629292302e-01  0.00000000000000000e+00
-bond_hamiltonian = -5.43694699199371301e-01  0.00000000000000000e+00
-SzSz             = -3.16338023249131073e-01  0.00000000000000000e+00
-SxSx             = -8.55764725464009945e-02  0.00000000000000000e+00
-SySy             = -1.41780203403839261e-01  0.00000000000000000e+00
-SzSzSzSz         =  3.00538294519135732e-02  0.00000000000000000e+00
+Energy           = -5.43694699199365972e-01  0.00000000000000000e+00
+Sz               =  6.11534505262877059e-03  0.00000000000000000e+00
+Sx               = -1.18113776629296119e-01  0.00000000000000000e+00
+2Sz              =  1.22306901052575412e-02  0.00000000000000000e+00
+bond_hamiltonian = -5.43694699199365972e-01  0.00000000000000000e+00
+SzSz             = -3.16338023249127298e-01  0.00000000000000000e+00
+SxSx             = -8.55764725463981218e-02  0.00000000000000000e+00
+SySy             = -1.41780203403840510e-01  0.00000000000000000e+00
+2SzSz            = -6.32676046498254596e-01  0.00000000000000000e+00
+SzSzSzSz         =  3.00538294519129001e-02  0.00000000000000000e+00
+2SzSzSzSz        =  6.01076589038258002e-02  0.00000000000000000e+00
diff --git a/test/data/output_AntiferroHeisenberg_real/multisite_obs_4.dat b/test/data/output_AntiferroHeisenberg_real/multisite_obs_4.dat
index 73747088..23e78d33 100644
--- a/test/data/output_AntiferroHeisenberg_real/multisite_obs_4.dat
+++ b/test/data/output_AntiferroHeisenberg_real/multisite_obs_4.dat
@@ -11,8 +11,13 @@
 # $10: imag
 # The names of op_group are the following: 
 # 0: SzSzSzSz        
+# 1: 2SzSzSzSz       
 
-0 0 1 0 1 1 0 1 2.99570527341487293e-02 0.00000000000000000e+00
-0 1 1 0 1 1 0 1 3.00861555469653479e-02 0.00000000000000000e+00
-0 2 1 0 1 1 0 1 3.00214333584342373e-02 0.00000000000000000e+00
-0 3 1 0 1 1 0 1 3.01506761681059714e-02 0.00000000000000000e+00
+0 0 1 0 1 1 0 1 2.99570527341480666e-02 0.00000000000000000e+00
+0 1 1 0 1 1 0 1 3.00861555469647268e-02 0.00000000000000000e+00
+0 2 1 0 1 1 0 1 3.00214333584335157e-02 0.00000000000000000e+00
+0 3 1 0 1 1 0 1 3.01506761681052948e-02 0.00000000000000000e+00
+1 0 1 0 1 1 0 1 5.99141054682961333e-02 0.00000000000000000e+00
+1 1 1 0 1 1 0 1 6.01723110939294537e-02 0.00000000000000000e+00
+1 2 1 0 1 1 0 1 6.00428667168670313e-02 0.00000000000000000e+00
+1 3 1 0 1 1 0 1 6.03013523362105897e-02 0.00000000000000000e+00
diff --git a/test/data/output_AntiferroHeisenberg_real/onesite_obs.dat b/test/data/output_AntiferroHeisenberg_real/onesite_obs.dat
index 26109d50..7e62ce11 100644
--- a/test/data/output_AntiferroHeisenberg_real/onesite_obs.dat
+++ b/test/data/output_AntiferroHeisenberg_real/onesite_obs.dat
@@ -4,19 +4,24 @@
 # $3: real
 # $4: imag
 # The names of op_group are the following: 
-# 0: Sz         
-# 1: Sx         
+# 0: Sz              
+# 1: Sx              
+# 2: 2Sz             
 # -1: norm
 
-0 0 3.82993056788538233e-01 0.00000000000000000e+00
-0 1 -3.89547536347500889e-01 0.00000000000000000e+00
-0 2 -3.45608673013142298e-01 0.00000000000000000e+00
-0 3 3.76624532782616039e-01 0.00000000000000000e+00
-1 0 -2.04721312181347537e-01 0.00000000000000000e+00
-1 1 -1.27047473942019484e-01 0.00000000000000000e+00
-1 2 -2.38535026007565459e-01 0.00000000000000000e+00
-1 3 9.78487056137541805e-02 0.00000000000000000e+00
--1 0 7.06065905040426989e-01 0.00000000000000000e+00
--1 1 7.43593497668431858e-01 0.00000000000000000e+00
--1 2 7.51167269076829069e-01 0.00000000000000000e+00
--1 3 6.72513272653018523e-01 0.00000000000000000e+00
+0 0 3.82993056788538955e-01 0.00000000000000000e+00
+0 1 -3.89547536347500223e-01 0.00000000000000000e+00
+0 2 -3.45608673013137857e-01 0.00000000000000000e+00
+0 3 3.76624532782614208e-01 0.00000000000000000e+00
+1 0 -2.04721312181346732e-01 0.00000000000000000e+00
+1 1 -1.27047473942022121e-01 0.00000000000000000e+00
+1 2 -2.38535026007569151e-01 0.00000000000000000e+00
+1 3 9.78487056137536115e-02 0.00000000000000000e+00
+2 0 7.65986113577077909e-01 0.00000000000000000e+00
+2 1 -7.79095072695000446e-01 0.00000000000000000e+00
+2 2 -6.91217346026275714e-01 0.00000000000000000e+00
+2 3 7.53249065565228415e-01 0.00000000000000000e+00
+-1 0 7.06065905040425768e-01 0.00000000000000000e+00
+-1 1 7.43593497668432746e-01 0.00000000000000000e+00
+-1 2 7.51167269076826738e-01 0.00000000000000000e+00
+-1 3 6.72513272653016414e-01 0.00000000000000000e+00
diff --git a/test/data/output_AntiferroHeisenberg_real/parameters.dat b/test/data/output_AntiferroHeisenberg_real/parameters.dat
index 151a9543..61dc847c 100644
--- a/test/data/output_AntiferroHeisenberg_real/parameters.dat
+++ b/test/data/output_AntiferroHeisenberg_real/parameters.dat
@@ -22,6 +22,8 @@ use_rsvd = false
 rsvd_oversampling_factor = 2
 meanfield_env = false
 
+mode = ground state
+simple
 Lcor = 0
 seed = 11
 is_real = 1
@@ -34,4 +36,4 @@ outdir = output_AntiferroHeisenberg_real
 Lsub = [ 2 , 2 ]
 skew = 0
 
-start_datetime =  2023-06-07T16:31:03+09:00
+start_datetime =  2024-01-15T23:23:01+09:00
diff --git a/test/data/output_AntiferroHeisenberg_real/twosite_obs.dat b/test/data/output_AntiferroHeisenberg_real/twosite_obs.dat
index 93a66d7a..ecf9697c 100644
--- a/test/data/output_AntiferroHeisenberg_real/twosite_obs.dat
+++ b/test/data/output_AntiferroHeisenberg_real/twosite_obs.dat
@@ -6,49 +6,58 @@
 # $5: real
 # $6: imag
 # The names of op_group are the following: 
-# 0: hamiltonian
-# 1: SzSz       
-# 2: SxSx       
-# 3: SySy       
+# 0: bond_hamiltonian
+# 1: SzSz            
+# 2: SxSx            
+# 3: SySy            
+# 4: 2SzSz           
 # -1: norm
 
-0 0 0 1 -1.66584129761267519e-01 0.00000000000000000e+00
-0 0 1 0 -2.61373275291908735e-01 0.00000000000000000e+00
-0 1 0 1 -3.21160656464442973e-01 0.00000000000000000e+00
-0 1 1 0 -2.62784471088295724e-01 0.00000000000000000e+00
-0 2 0 1 -1.67312423722473624e-01 0.00000000000000000e+00
-0 2 1 0 -3.35067831613584444e-01 0.00000000000000000e+00
-0 3 0 1 -3.22957384828300387e-01 0.00000000000000000e+00
-0 3 1 0 -3.37538624027198475e-01 0.00000000000000000e+00
-1 0 0 1 -1.33324968627194868e-01 0.00000000000000000e+00
-1 0 1 0 -1.61814083059259678e-01 0.00000000000000000e+00
-1 1 0 1 -1.71118008938635324e-01 0.00000000000000000e+00
-1 1 1 0 -1.62023966039101103e-01 0.00000000000000000e+00
-1 2 0 1 -1.33365169593474941e-01 0.00000000000000000e+00
-1 2 1 0 -1.65776212997030326e-01 0.00000000000000000e+00
-1 3 0 1 -1.71537906054280792e-01 0.00000000000000000e+00
-1 3 1 0 -1.66391777687539821e-01 0.00000000000000000e+00
-2 0 0 1 1.69979452151880171e-02 0.00000000000000000e+00
-2 0 1 0 -2.68075650106709765e-02 0.00000000000000000e+00
-2 1 0 1 -7.43982975314806949e-02 0.00000000000000000e+00
-2 1 1 0 -2.73263995592405579e-02 0.00000000000000000e+00
-2 2 0 1 1.67249333950529773e-02 0.00000000000000000e+00
-2 2 1 0 -8.57656256668481581e-02 0.00000000000000000e+00
-2 3 0 1 -7.50642098592703699e-02 0.00000000000000000e+00
-2 3 1 0 -8.66666711683256874e-02 0.00000000000000000e+00
-3 0 0 1 -5.02571063492606718e-02 0.00000000000000000e+00
-3 0 1 0 -7.27516272219781851e-02 0.00000000000000000e+00
-3 1 0 1 -7.56443499943268149e-02 0.00000000000000000e+00
-3 1 1 0 -7.34341054899541185e-02 0.00000000000000000e+00
-3 2 0 1 -5.06721875240518163e-02 0.00000000000000000e+00
-3 2 1 0 -8.35259929497060571e-02 0.00000000000000000e+00
-3 3 0 1 -7.63552689147493080e-02 0.00000000000000000e+00
-3 3 1 0 -8.44801751713327859e-02 0.00000000000000000e+00
--1 0 0 1 5.15823310085911979e-01 0.00000000000000000e+00
--1 0 1 0 5.27867949487865862e-01 0.00000000000000000e+00
--1 1 0 1 5.15206590510061679e-01 0.00000000000000000e+00
--1 1 1 0 4.86751317029447073e-01 0.00000000000000000e+00
--1 2 0 1 4.88534553522139314e-01 0.00000000000000000e+00
--1 2 1 0 5.27355982720729588e-01 0.00000000000000000e+00
--1 3 0 1 4.88243759924334775e-01 0.00000000000000000e+00
--1 3 1 0 4.86525799277800153e-01 0.00000000000000000e+00
+0 0 0 1 -1.66584129761265548e-01 0.00000000000000000e+00
+0 0 1 0 -2.61373275291908513e-01 0.00000000000000000e+00
+0 1 0 1 -3.21160656464443139e-01 0.00000000000000000e+00
+0 1 1 0 -2.62784471088293947e-01 0.00000000000000000e+00
+0 2 0 1 -1.67312423722470932e-01 0.00000000000000000e+00
+0 2 1 0 -3.35067831613582723e-01 0.00000000000000000e+00
+0 3 0 1 -3.22957384828299499e-01 0.00000000000000000e+00
+0 3 1 0 -3.37538624027199752e-01 0.00000000000000000e+00
+1 0 0 1 -1.33324968627193452e-01 0.00000000000000000e+00
+1 0 1 0 -1.61814083059259706e-01 0.00000000000000000e+00
+1 1 0 1 -1.71118008938634658e-01 0.00000000000000000e+00
+1 1 1 0 -1.62023966039100881e-01 0.00000000000000000e+00
+1 2 0 1 -1.33365169593473304e-01 0.00000000000000000e+00
+1 2 1 0 -1.65776212997028355e-01 0.00000000000000000e+00
+1 3 0 1 -1.71537906054279987e-01 0.00000000000000000e+00
+1 3 1 0 -1.66391777687538794e-01 0.00000000000000000e+00
+2 0 0 1 1.69979452151889088e-02 0.00000000000000000e+00
+2 0 1 0 -2.68075650106703658e-02 0.00000000000000000e+00
+2 1 0 1 -7.43982975314810419e-02 0.00000000000000000e+00
+2 1 1 0 -2.73263995592394823e-02 0.00000000000000000e+00
+2 2 0 1 1.67249333950540459e-02 0.00000000000000000e+00
+2 2 1 0 -8.57656256668478112e-02 0.00000000000000000e+00
+2 3 0 1 -7.50642098592703005e-02 0.00000000000000000e+00
+2 3 1 0 -8.66666711683264507e-02 0.00000000000000000e+00
+3 0 0 1 -5.02571063492610673e-02 0.00000000000000000e+00
+3 0 1 0 -7.27516272219783794e-02 0.00000000000000000e+00
+3 1 0 1 -7.56443499943273423e-02 0.00000000000000000e+00
+3 1 1 0 -7.34341054899534801e-02 0.00000000000000000e+00
+3 2 0 1 -5.06721875240516845e-02 0.00000000000000000e+00
+3 2 1 0 -8.35259929497065290e-02 0.00000000000000000e+00
+3 3 0 1 -7.63552689147491831e-02 0.00000000000000000e+00
+3 3 1 0 -8.44801751713343679e-02 0.00000000000000000e+00
+4 0 0 1 -2.66649937254386904e-01 0.00000000000000000e+00
+4 0 1 0 -3.23628166118519411e-01 0.00000000000000000e+00
+4 1 0 1 -3.42236017877269316e-01 0.00000000000000000e+00
+4 1 1 0 -3.24047932078201761e-01 0.00000000000000000e+00
+4 2 0 1 -2.66730339186946608e-01 0.00000000000000000e+00
+4 2 1 0 -3.31552425994056710e-01 0.00000000000000000e+00
+4 3 0 1 -3.43075812108559974e-01 0.00000000000000000e+00
+4 3 1 0 -3.32783555375077589e-01 0.00000000000000000e+00
+-1 0 0 1 5.15823310085911646e-01 0.00000000000000000e+00
+-1 0 1 0 5.27867949487862531e-01 0.00000000000000000e+00
+-1 1 0 1 5.15206590510061568e-01 0.00000000000000000e+00
+-1 1 1 0 4.86751317029445851e-01 0.00000000000000000e+00
+-1 2 0 1 4.88534553522136039e-01 0.00000000000000000e+00
+-1 2 1 0 5.27355982720726590e-01 0.00000000000000000e+00
+-1 3 0 1 4.88243759924331056e-01 0.00000000000000000e+00
+-1 3 1 0 4.86525799277798876e-01 0.00000000000000000e+00
diff --git a/tool/tenes_std.py b/tool/tenes_std.py
index b6560a00..240a072d 100644
--- a/tool/tenes_std.py
+++ b/tool/tenes_std.py
@@ -381,7 +381,9 @@ def check(self) -> None:
             Raises RuntimeError if any information is invalid.
         """
         if not (isinstance(self.L, list) and len(self.L) == 2 and all_positive(self.L)):
-            msg = "L_sub should be a positive integer or a list with 2 positive integers"
+            msg = (
+                "L_sub should be a positive integer or a list with 2 positive integers"
+            )
             raise RuntimeError(msg)
 
         failed = False
@@ -581,7 +583,7 @@ def __init__(
         *,
         elements: Optional[np.ndarray] = None,
         ops: Optional[List[int]] = None,
-        group: Optional[int] = None
+        group: Optional[int] = None,
     ):
         self.bond = bond
         self.group = group
@@ -630,14 +632,26 @@ class OnesiteObservable:
     elements: np.ndarray
     sites: List[int]
     name: str
+    coeff: float
+    coeff_im: float
 
-    def __init__(self, group: int, elements: np.ndarray, sites: List[int], name: str):
+    def __init__(
+        self,
+        group: int,
+        elements: np.ndarray,
+        sites: List[int],
+        name: str = "",
+        coeff: float = 1.0,
+        coeff_im: float = 0.0,
+    ):
         self.group = group
         assert elements.ndim == 2
         assert elements.shape[0] == elements.shape[1]
         self.elements = elements
         self.sites = sites
         self.name = name
+        self.coeff = coeff
+        self.coeff_im = coeff_im
 
     def to_toml_strs(self) -> List[str]:
         ret = []
@@ -663,6 +677,8 @@ def to_toml_strs(self) -> List[str]:
             ret.append(line)
             it.iternext()
         ret.append('"""')
+        ret.append("coeff = {}".format(self.coeff))
+        ret.append("coeff_im = {}".format(self.coeff_im))
         return ret
 
 
@@ -672,6 +688,8 @@ class TwositeObservable:
     elements: Optional[np.ndarray]
     ops: Optional[List[int]]
     name: str
+    coeff: float
+    coeff_re: float
 
     def __init__(
         self,
@@ -680,7 +698,9 @@ def __init__(
         *,
         elements: np.ndarray = None,
         ops: List[int] = None,
-        name: str = ""
+        name: str = "",
+        coeff: float = 1.0,
+        coeff_im: float = 0.0,
     ):
         self.group = group
         if elements is not None:
@@ -697,6 +717,8 @@ def __init__(
             self.ops = ops
         self.bonds = bonds
         self.name = name
+        self.coeff = coeff
+        self.coeff_im = coeff_im
 
     def to_toml_strs(self) -> List[str]:
         ret = []
@@ -728,6 +750,8 @@ def to_toml_strs(self) -> List[str]:
             ret.append('"""')
         else:
             ret.append("ops = {}".format(self.ops))
+        ret.append("coeff = {}".format(self.coeff))
+        ret.append("coeff_im = {}".format(self.coeff_im))
         return ret
 
     def to_twosite_operators(self) -> List[NNOperator]:
@@ -742,9 +766,17 @@ class MultisiteObservable:
     multisites: List[Multisite]
     ops: List[int]
     name: str
+    coeff: float
+    coeff_im: float
 
     def __init__(
-        self, group: int, multisites: List[Multisite], ops: List[int], name: str = ""
+        self,
+        group: int,
+        multisites: List[Multisite],
+        ops: List[int],
+        name: str = "",
+        coeff: float = 1.0,
+        coeff_im: float = 0.0,
     ):
         self.group = group
         self.multisites = multisites
@@ -753,6 +785,8 @@ def __init__(
                 raise ValueError("Multisites have different number of sites")
         self.ops = ops
         self.name = name
+        self.coeff = coeff
+        self.coeff_im = coeff_im
 
     def nsites(self) -> int:
         return self.multisites[0].nsites()
@@ -764,11 +798,13 @@ def to_toml_strs(self) -> List[str]:
         ret.append('multisites = """')
         for ms in self.multisites:
             line = str(ms.source_site)
-            for i in range(ms.nsites()-1):
+            for i in range(ms.nsites() - 1):
                 line += f" {ms.dx[i]} {ms.dy[i]}"
             ret.append(line)
         ret.append('"""')
         ret.append("ops = {}".format(self.ops))
+        ret.append("coeff = {}".format(self.coeff))
+        ret.append("coeff_im = {}".format(self.coeff_im))
         return ret
 
 
@@ -809,8 +845,8 @@ def make_evolution_twosite(
         source = hamiltonian.bond.source_site
         dx = hamiltonian.bond.dx
         dy = hamiltonian.bond.dy
-        msg =  f"A bond term of Hamiltonian connects a source site {source} and a target site (dx, dy) = ({dx}, {dy}) "
-        msg +=  "but they are disconnected. please check the dimensions of virtual bonds (D=1 bonds are disconnected)."
+        msg = f"A bond term of Hamiltonian connects a source site {source} and a target site (dx, dy) = ({dx}, {dy}) "
+        msg += "but they are disconnected. please check the dimensions of virtual bonds (D=1 bonds are disconnected)."
         raise RuntimeError(msg)
 
     if nhops == 1: