Hubbard Model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "59f3e744",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MPO\n",
       "[1] ((dim=5|id=161|\"Link,l=1\"), (dim=2|id=635|\"Boson,Site,n=1\")', (dim=2|id=635|\"Boson,Site,n=1\"))\n",
       "[2] ((dim=5|id=161|\"Link,l=1\"), (dim=6|id=885|\"Link,l=2\"), (dim=2|id=835|\"Boson,Site,n=2\")', (dim=2|id=835|\"Boson,Site,n=2\"))\n",
       "[3] ((dim=6|id=885|\"Link,l=2\"), (dim=7|id=508|\"Link,l=3\"), (dim=2|id=604|\"Boson,Site,n=3\")', (dim=2|id=604|\"Boson,Site,n=3\"))\n",
       "[4] ((dim=7|id=508|\"Link,l=3\"), (dim=6|id=869|\"Link,l=4\"), (dim=2|id=638|\"Boson,Site,n=4\")', (dim=2|id=638|\"Boson,Site,n=4\"))\n",
       "[5] ((dim=6|id=869|\"Link,l=4\"), (dim=5|id=694|\"Link,l=5\"), (dim=2|id=420|\"Boson,Site,n=5\")', (dim=2|id=420|\"Boson,Site,n=5\"))\n",
       "[6] ((dim=5|id=694|\"Link,l=5\"), (dim=2|id=315|\"Boson,Site,n=6\")', (dim=2|id=315|\"Boson,Site,n=6\"))\n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using ITensors\n",
    "function two_component_BH(N::Int64;U=1.0,U12=-0.5,t1=0.5,t2=0.25,kwargs...)\n",
    "    sites = siteinds(\"Boson\",N;conserve_qns=true,conserve_number=false)\n",
    "    op = OpSum()\n",
    "    for i in 1:2:N-3\n",
    "        op += -U/2, \"N\", i\n",
    "        op += U/2, \"N\", i,\"N\",i\n",
    "        op += -t1, \"a\", i, \"a†\", i + 2\n",
    "        op += -t1, \"a†\", i, \"a\", i + 2\n",
    "    end\n",
    "    op += -U/2, \"N\", N-1\n",
    "    op += U/2, \"N\", N-1,\"N\",N-1\n",
    "\n",
    "    for i in 2:2:N-2\n",
    "        op += -U/2, \"N\", i\n",
    "        op += U/2, \"N\", i,\"N\",i\n",
    "        op += -t2, \"a\", i, \"a†\", i + 2\n",
    "        op += -t2, \"a†\", i, \"a\", i + 2\n",
    "    end\n",
    "    op += -U/2, \"N\", N\n",
    "    op += U/2, \"N\", N,\"N\",N\n",
    "\n",
    "    for i in 1:2:N-1\n",
    "        op +=U12, \"N\", i,\"N\",i+1\n",
    "    end\n",
    "    MPO(op,sites;kwargs...)\n",
    "end\n",
    "\n",
    "two_component_BH(6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "id": "a9ae8932",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MPO\n",
       "[1] ((dim=5|id=679|\"Link,l=1\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=2|id=472|\"Boson,Site,n=1\")' <Out>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1, (dim=2|id=472|\"Boson,Site,n=1\") <In>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1)\n",
       "[2] ((dim=5|id=679|\"Link,l=1\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=5|id=845|\"Link,l=2\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=2|id=746|\"Boson,Site,n=2\")' <Out>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1, (dim=2|id=746|\"Boson,Site,n=2\") <In>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1)\n",
       "[3] ((dim=5|id=845|\"Link,l=2\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=5|id=627|\"Link,l=3\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=2|id=553|\"Boson,Site,n=3\")' <Out>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1, (dim=2|id=553|\"Boson,Site,n=3\") <In>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1)\n",
       "[4] ((dim=5|id=627|\"Link,l=3\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=5|id=559|\"Link,l=4\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=2|id=866|\"Boson,Site,n=4\")' <Out>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1, (dim=2|id=866|\"Boson,Site,n=4\") <In>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1)\n",
       "[5] ((dim=5|id=559|\"Link,l=4\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=5|id=327|\"Link,l=5\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=2|id=535|\"Boson,Site,n=5\")' <Out>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1, (dim=2|id=535|\"Boson,Site,n=5\") <In>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1)\n",
       "[6] ((dim=5|id=327|\"Link,l=5\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN(\"Number\",0) => 1\n",
       " 3: QN(\"Number\",-1) => 1\n",
       " 4: QN(\"Number\",1) => 1\n",
       " 5: QN(\"Number\",0) => 1, (dim=2|id=624|\"Boson,Site,n=6\")' <Out>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1, (dim=2|id=624|\"Boson,Site,n=6\") <In>\n",
       " 1: QN(\"Number\",0) => 1\n",
       " 2: QN(\"Number\",1) => 1)\n"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using ITensors\n",
    "function one_component_BH(M::Int64,sites;U=1.0,J=0.5,mu=0,V =0,kwargs...)\n",
    "    sites = sites\n",
    "    op = OpSum()\n",
    "    for i in 1:M-1\n",
    "        op += -mu -U/2, \"N\", i\n",
    "        op += U/2, \"N\", i,\"N\",i\n",
    "        op += -J, \"a\", i, \"a†\", i + 1\n",
    "        op += -J, \"a†\", i, \"a\", i + 1\n",
    "        op += V, \"N\", i,\"N\", i+1\n",
    "    end\n",
    "    op += -mu-U/2, \"N\", M\n",
    "    op += U/2, \"N\", M,\"N\",M\n",
    "    \n",
    "    MPO(op,sites;kwargs...)\n",
    "end\n",
    "\n",
    "sites = siteinds(\"Boson\",6;conserve_qns=true)\n",
    "one_component_BH(6,sites)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "id": "cda37deb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MPO\n",
       "[1] ((dim=6|id=985|\"Link,l=1\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=4|id=561|\"Electron,Site,n=1\")' <Out>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1, (dim=4|id=561|\"Electron,Site,n=1\") <In>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1)\n",
       "[2] ((dim=6|id=985|\"Link,l=1\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=6|id=747|\"Link,l=2\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=4|id=404|\"Electron,Site,n=2\")' <Out>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1, (dim=4|id=404|\"Electron,Site,n=2\") <In>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1)\n",
       "[3] ((dim=6|id=747|\"Link,l=2\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=6|id=183|\"Link,l=3\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=4|id=245|\"Electron,Site,n=3\")' <Out>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1, (dim=4|id=245|\"Electron,Site,n=3\") <In>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1)\n",
       "[4] ((dim=6|id=183|\"Link,l=3\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=6|id=603|\"Link,l=4\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=4|id=889|\"Electron,Site,n=4\")' <Out>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1, (dim=4|id=889|\"Electron,Site,n=4\") <In>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1)\n",
       "[5] ((dim=6|id=603|\"Link,l=4\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=6|id=659|\"Link,l=5\") <Out>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=4|id=519|\"Electron,Site,n=5\")' <Out>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1, (dim=4|id=519|\"Electron,Site,n=5\") <In>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1)\n",
       "[6] ((dim=6|id=659|\"Link,l=5\") <In>\n",
       " 1: QN() => 1\n",
       " 2: QN((\"Nf\",-1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 4: QN((\"Nf\",-1,-1),(\"Sz\",-1)) => 1\n",
       " 5: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 6: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1, (dim=4|id=891|\"Electron,Site,n=6\")' <Out>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1, (dim=4|id=891|\"Electron,Site,n=6\") <In>\n",
       " 1: QN((\"Nf\",0,-1),(\"Sz\",0)) => 1\n",
       " 2: QN((\"Nf\",1,-1),(\"Sz\",1)) => 1\n",
       " 3: QN((\"Nf\",1,-1),(\"Sz\",-1)) => 1\n",
       " 4: QN((\"Nf\",2,-1),(\"Sz\",0)) => 1)\n"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using ITensors\n",
    "function one_component_FH(M::Int64,sites;U=1.0,J=0.5,mu=0,kwargs...)\n",
    "    sites = sites\n",
    "    op = OpSum()\n",
    "    for i in 1:M-1\n",
    "        op += -mu, \"n↑\", i\n",
    "        op += -mu, \"n↓\", i\n",
    "        op += U, \"n↑\", i,\"n↓\",i\n",
    "        op += -J, \"c↑\", i, \"c†↑\", i + 1\n",
    "        op += -J, \"c†↑\", i, \"c↑\", i + 1\n",
    "        op += -J, \"c↓\", i, \"c†↓\", i + 1\n",
    "        op += -J, \"c†↓\", i, \"c↓\", i + 1\n",
    "    end\n",
    "    op += -mu, \"n↑\", M\n",
    "    op += -mu, \"n↓\", M\n",
    "    op += U, \"n↑\", M,\"n↓\",M\n",
    "    \n",
    "    MPO(op,sites;kwargs...)\n",
    "end\n",
    "\n",
    "sites = siteinds(\"Electron\",6;conserve_qns=true)\n",
    "one_component_FH(6,sites)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "id": "ba945f20",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[\"UpDn\", \"UpDn\", \"UpDn\", \"UpDn\", \"UpDn\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\", \"0\"]\n",
      "After sweep 1 energy=20.221708117562546  maxlinkdim=6 maxerr=8.50E-11 time=0.070\n",
      "After sweep 2 energy=9.77227568989377  maxlinkdim=34 maxerr=8.43E-11 time=0.225\n",
      "After sweep 3 energy=0.009644227787431223  maxlinkdim=50 maxerr=1.20E-07 time=0.421\n",
      "After sweep 4 energy=-9.930792552327851  maxlinkdim=50 maxerr=1.12E-07 time=0.545\n",
      "After sweep 5 energy=-9.929287969190497  maxlinkdim=50 maxerr=5.47E-08 time=1.359\n",
      "After sweep 6 energy=-9.795327105003341  maxlinkdim=50 maxerr=3.30E-06 time=0.653\n",
      "After sweep 7 energy=-9.702670682315437  maxlinkdim=50 maxerr=1.25E-05 time=0.709\n",
      "After sweep 8 energy=-9.776045040478941  maxlinkdim=50 maxerr=3.85E-06 time=0.804\n",
      "After sweep 9 energy=-9.85084451989099  maxlinkdim=50 maxerr=3.72E-06 time=0.833\n",
      "After sweep 10 energy=-10.084869514364952  maxlinkdim=50 maxerr=2.09E-06 time=0.851\n",
      "After sweep 11 energy=-9.675494722321767  maxlinkdim=50 maxerr=3.10E-06 time=1.520\n",
      "After sweep 12 energy=-9.831697867598631  maxlinkdim=50 maxerr=3.85E-06 time=0.793\n",
      "After sweep 13 energy=-10.15190308436711  maxlinkdim=50 maxerr=7.81E-06 time=0.811\n",
      "After sweep 14 energy=-10.145639663311991  maxlinkdim=50 maxerr=4.94E-06 time=0.865\n",
      "After sweep 15 energy=-10.2564664797576  maxlinkdim=50 maxerr=4.30E-06 time=0.904\n",
      "After sweep 16 energy=-10.359952121209616  maxlinkdim=50 maxerr=4.24E-06 time=1.514\n",
      "After sweep 17 energy=-10.383577153004351  maxlinkdim=50 maxerr=4.93E-06 time=0.820\n",
      "After sweep 18 energy=-10.414488666705957  maxlinkdim=50 maxerr=3.81E-06 time=0.886\n",
      "After sweep 19 energy=-10.432477116640122  maxlinkdim=50 maxerr=3.14E-06 time=0.902\n",
      "After sweep 20 energy=-10.55584742529333  maxlinkdim=50 maxerr=2.41E-06 time=1.583\n",
      "n = [1.4035354248985725, 1.6813176736691113, 1.707461161433771, 1.7109446120028762, 1.7116098192448592, 1.7116241230167468, 1.7108322527115243, 1.707363756211666, 1.6812845186638516, 1.403582289276246]\n",
      "Sz = [-0.032484107958704246, -0.18138426002495112, 0.02759445391734982, 0.0477957568080247, 0.0699597117516644, 0.05841530215330639, -0.08189659988245321, -0.021912959718061044, 0.0781752740057082, -0.059340426649462825, -0.02994571090556362, 0.07150647565429649, 0.018831790808718087, -0.06796241249127477, 0.0063925730058090715, 0.07867864614068222, 0.03890423428274999, 0.046237599334186294, -0.03073865989492266, -0.036826680337102]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "20-element Vector{Float64}:\n",
       " -0.032484107958704246\n",
       " -0.18138426002495112\n",
       "  0.02759445391734982\n",
       "  0.0477957568080247\n",
       "  0.0699597117516644\n",
       "  0.05841530215330639\n",
       " -0.08189659988245321\n",
       " -0.021912959718061044\n",
       "  0.0781752740057082\n",
       " -0.059340426649462825\n",
       " -0.02994571090556362\n",
       "  0.07150647565429649\n",
       "  0.018831790808718087\n",
       " -0.06796241249127477\n",
       "  0.0063925730058090715\n",
       "  0.07867864614068222\n",
       "  0.03890423428274999\n",
       "  0.046237599334186294\n",
       " -0.03073865989492266\n",
       " -0.036826680337102"
      ]
     },
     "execution_count": 309,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let\n",
    "    N = 20\n",
    "    flux = 10\n",
    "    sites = siteinds(\"Electron\",N;conserve_qns=true)\n",
    "    state = [n<=flux/2 ? \"UpDn\" : \"0\" for n in 1:N]\n",
    "    println(state)\n",
    "    H = one_component_FH(N,sites;U=10,J=0.2,mu=1)\n",
    "    psi0 = randomMPS(sites,state)\n",
    "    nsweeps = 20\n",
    "    maxdim = 50 #[10,20,100,100,200]\n",
    "    cutoff = [1E-10]\n",
    "\n",
    "    energy, psi = dmrg(H,psi0; nsweeps, maxdim, cutoff)\n",
    "    order = expect(psi,\"Ntot\")\n",
    "    Sz = expect(psi,\"Sz\")\n",
    "    #cor = correlation_matrix(psi,\"a\",\"a\")\n",
    "    \n",
    "    #for j in 1:N\n",
    "    #    orthogonalize!(psi,j);\n",
    "    #    ket = psi[j]\n",
    "    #    bra = dag(prime(ket,\"Site\"));\n",
    "    #    ampo_b= op(sites,\"a\",j)\n",
    "    #    println(scalar(bra*ampo_b*ket))\n",
    "    #end\n",
    "    \n",
    "    #@show order\n",
    "    @show n\n",
    "    #@show cor\n",
    "    @show Sz\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "id": "2c1540ed",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum = 10.000000000018616\n",
      "sum = 10.00000000068296\n",
      "sum = 10.000000037313727\n",
      "sum = 10.000000399217866\n",
      "sum = 10.000002145561366\n",
      "sum = 10.000986868395238\n",
      "sum = 10.645269296370275\n",
      "sum = 11.454024727669205\n",
      "sum = 11.97564545092986\n",
      "sum = 12.511111234776399\n",
      "sum = 12.927249541319586\n",
      "sum = 13.309849528398857\n",
      "sum = 13.675525265246646\n",
      "sum = 14.03032729711512\n",
      "sum = 14.378557161933303\n",
      "sum = 14.722566731485264\n",
      "sum = 15.064733337859069\n",
      "sum = 15.406796157614325\n",
      "sum = 15.74742454782061\n",
      "sum = 16.08788960395129\n",
      "sum = 16.429555631129226\n"
     ]
    }
   ],
   "source": [
    "for Ji in 0:0.02:0.4\n",
    "    N = 10\n",
    "    sites = siteinds(\"Boson\",N;conserve_qns=false,dim=11)\n",
    "    H = one_component_BH(N,sites;U=1,J=Ji,mu=0.6)\n",
    "    psi0 = randomMPS(sites)\n",
    "    nsweeps = 50\n",
    "    maxdim = 3\n",
    "    cutoff = [1E-10]\n",
    "\n",
    "    energy, psi = dmrg(H,psi0; nsweeps, maxdim, cutoff, outputlevel = 0)\n",
    "    order = expect(psi,\"a\")\n",
    "    n = expect(psi,\"n\")\n",
    "    cor = correlation_matrix(psi,\"n\",\"n\")\n",
    "    \n",
    "    sum = 0.0    \n",
    "    for i in 1:length(n)\n",
    "        sum += n[i]\n",
    "    end\n",
    "    @show sum\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62c7c3ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "-0.7403566002809007 > 0.5\n",
    "-0.4601053423129124 > 1\n",
    "-0.4294202230264739 > 1.5\n",
    "-0.011024562694459443 > 2\n",
    "0.43693169091446427 > 2.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b3af109",
   "metadata": {},
   "outputs": [],
   "source": [
    "0 > 0\n",
    "8.758504955648722e-7 > 0.05\n",
    "-0.36632788099079 > 0.1\n",
    "-0.10132456409560177 > 0.15\n",
    "-0.004468749329044437 > 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 336,
   "id": "0392efcc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mag1 = [0.25; 0.24955629299160814; 0.2482165434955703; 0.24595392720250056; 0.24271947260412963; 0.23843219676046265; 0.23295951755403035; 0.22608507168670347; 0.21746620261470198; 0.2065936745028841; 0.19278500157887024; 0.17527213612827858; 0.15341776833349047; 0.12690630189454086; 0.10038306010039451; 0.08212677178291336; 0.06936253000298684; 0.05976133513919801; 0.052252389959278396; 0.046224918622775724; 0.04129005996049463;;]\n",
      "mag2 = [0.25; 0.24955843758642676; 0.24822500623526558; 0.24597221961358545; 0.24274891280236438; 0.23846833026098774; 0.23298411170147618; 0.22604781056872156; 0.217240352743904; 0.20586615073813577; 0.1907802517848158; 0.17003995606463593; 0.13966116123314187; 0.08807399255340147; 0.024522294806447822; 0.004150365248369304; 0.0008542506552955673; 0.000249781051162786; 0.00010053718049776244; 5.240842765004733e-5; 3.1979483737044575e-5;;]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "21×1 Matrix{Float64}:\n",
       " 0.25\n",
       " 0.24955843758642676\n",
       " 0.24822500623526558\n",
       " 0.24597221961358545\n",
       " 0.24274891280236438\n",
       " 0.23846833026098774\n",
       " 0.23298411170147618\n",
       " 0.22604781056872156\n",
       " 0.217240352743904\n",
       " 0.20586615073813577\n",
       " 0.1907802517848158\n",
       " 0.17003995606463593\n",
       " 0.13966116123314187\n",
       " 0.08807399255340147\n",
       " 0.024522294806447822\n",
       " 0.004150365248369304\n",
       " 0.0008542506552955673\n",
       " 0.000249781051162786\n",
       " 0.00010053718049776244\n",
       " 5.240842765004733e-5\n",
       " 3.1979483737044575e-5"
      ]
     },
     "execution_count": 336,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mag1 = fill(0.0, (21,1))\n",
    "mag2 = fill(0.0, (21,1))\n",
    "i = 0\n",
    "for h in 0:0.05:1\n",
    "    i += 1\n",
    "    N = 50\n",
    "    J = 1\n",
    "    sites = siteinds(\"S=1/2\",N)\n",
    "\n",
    "    os = OpSum()\n",
    "    for i=1:N-1, j=i+1:N\n",
    "        os += -J/(j-i)^3,\"Sz\",i,\"Sz\",j\n",
    "    end\n",
    "    for i=1:N\n",
    "        os += -h,\"Sx\",i\n",
    "    end\n",
    "    H = MPO(os,sites)\n",
    "\n",
    "    psi0 = randomMPS(sites,10)\n",
    "\n",
    "    nsweeps = 30\n",
    "    maxdim = [10,20,100,100,200]\n",
    "    cutoff = [1E-10]\n",
    "\n",
    "    energy, psi = dmrg(H,psi0; nsweeps, maxdim, cutoff, outputlevel = 0)\n",
    "    M = expect(psi,\"Sz\")\n",
    "    corM = correlation_matrix(psi,\"Sz\",\"Sz\")\n",
    "    mag1[i] = corM[4,6]\n",
    "    mag2[i] = corM[4,40]\n",
    "    #sum1 = 0.0 \n",
    "    #sum2 = 0.0\n",
    "    #for i in 1:length(n)\n",
    "    #    for j in 1:length(n)\n",
    "    #        sum1 += corM[i,j]/N^2\n",
    "    #    end\n",
    "    #    sum2 += M[i]/N\n",
    "    #end\n",
    "end\n",
    "@show mag1\n",
    "@show mag2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "410da3df",
   "metadata": {},
   "outputs": [],
   "source": [
    "0.25000000000000017\n",
    "0.24934556259408522\n",
    "0.24736880700661054\n",
    "0.2440280489247058\n",
    "0.2392513418137069\n",
    "0.2329168901824174\n",
    "0.2247219432146044\n",
    "0.21425687831201734\n",
    "0.2007112534577526\n",
    "0.1832297644696703\n",
    "0.16190212759814424\n",
    "0.1388798561598818\n",
    "0.11748821824961303\n",
    "0.09988403222921954\n",
    "0.08634830293461469\n",
    "0.07617963945447138\n",
    "0.06851765099208885\n",
    "0.06265663628735213\n",
    "0.058085929081739034\n",
    "0.054450555806006294\n",
    "0.05150510955873902"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.9.0",
   "language": "julia",
   "name": "julia-1.9"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.9.0"
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 },
 "nbformat": 4,
 "nbformat_minor": 5
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