From d3376919b5be8c047207edb3ac1870eb0929d6ed Mon Sep 17 00:00:00 2001 From: TeNeS Developers Date: Wed, 11 Oct 2023 20:07:04 +0000 Subject: [PATCH] Deploy docs to develop by GitHub Actions triggered by e2f21a1d7399702bfd960abdf9106170b43462b8 --- .../_images/tutorial_07_timeevolution.png | Bin 0 -> 42293 bytes .../_images/tutorial_07_timeevolution_D10.png | Bin 0 -> 38132 bytes .../_images/tutorial_08_finitetemperature.png | Bin 0 -> 148939 bytes .../en/html/_sources/tutorial/index.rst.txt | 4 +- .../tutorial/simple_tutorial-7.rst.txt | 44 ++++ .../tutorial/simple_tutorial-8.rst.txt | 31 +++ .../en/html/file_specification/index.html | 4 +- manual/develop/en/html/index.html | 8 +- manual/develop/en/html/objects.inv | Bin 1743 -> 2037 bytes manual/develop/en/html/searchindex.js | 2 +- manual/develop/en/html/tutorial/index.html | 24 +- .../en/html/tutorial/simple_tutorial-1.html | 12 +- .../en/html/tutorial/simple_tutorial-5.html | 32 +-- .../en/html/tutorial/simple_tutorial-6.html | 28 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Contents4. Tutorial
  • 5. File format
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23, "specifi": 23, "compil": 23, "us": [23, 30], "pre": 23, "built": 23, "mptensor": 23, "python": 23, "interpret": 23, "tutori": 24, "Ising": [25, 28, 29], "transvers": [25, 28, 29], "magnet": [25, 26], "field": [25, 28, 29, 30], "process": 26, "heisenberg": [26, 30], "phase": 27, "diagram": 27, "hardcor": 27, "trianglar": 27, "real": 28, "definit": 30, "oper": 30, "standard": 30, "unit": 30, "cell": 30, "bond": 30, "site": 30, "antiferromagnet": 30, "stagger": 30}, "envversion": {"sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx": 58}, "alltitles": {"What is TeNeS ?": [[0, "what-is-tenes"]], "Overview": [[1, "overview"]], "Developers": [[1, "developers"]], "Version information": [[1, "version-information"]], "License": [[1, "license"]], "Papers": [[1, "papers"]], "Copyright": [[1, "copyright"]], "Acknowledgement": [[2, "acknowledgement"]], "Algorithm": [[3, "algorithm"]], "Tensor Network States": [[3, "tensor-network-states"]], "Contraction of iTPS": [[3, "contraction-of-itps"]], "Optimization of iTPS": [[3, "optimization-of-itps"]], "Contacts": [[5, "contacts"]], "FAQ": [[6, "faq"]], "Example": [[8, "example"], [9, "example"], [9, "id1"], [9, "id2"], [9, "id3"], [12, "example"], [12, "id1"], [14, "example"], [15, "example"], [16, "example"], [16, "id1"], [16, "id2"], [16, "id3"]], "Input file for tenes": [[9, "input-file-for-tenes"]], "parameter section": [[9, "parameter-section"], [15, "parameter-section"], [16, "parameter-section"]], "parameter.general": [[9, "parameter-general"], [14, "parameter-general"], [15, "parameter-general"], [16, "parameter-general"]], "parameter.simple_update": [[9, "parameter-simple-update"], [14, "parameter-simple-update"], [15, "parameter-simple-update"], [16, "parameter-simple-update"]], "parameter.full_update": [[9, "parameter-full-update"], [14, "parameter-full-update"], [15, "parameter-full-update"], [16, "parameter-full-update"]], "parameter.ctm": [[9, "parameter-ctm"], [14, "parameter-ctm"], [15, "parameter-ctm"], [16, "parameter-ctm"]], "parameter.random": [[9, "parameter-random"], [14, "parameter-random"], [15, "parameter-random"], [16, "parameter-random"]], "tensor section": [[9, "tensor-section"], [16, "tensor-section"]], "tensor.unitcell subsection": [[9, "tensor-unitcell-subsection"], [16, "tensor-unitcell-subsection"], [17, "tensor-unitcell-subsection"]], "observable section": [[9, "observable-section"], [16, "observable-section"]], "observable.onesite": [[9, "observable-onesite"], [12, "observable-onesite"], [16, "observable-onesite"]], "observable.twosite": [[9, "observable-twosite"], [12, "observable-twosite"], [16, "observable-twosite"]], "observable.multisite": [[9, "observable-multisite"], [12, "observable-multisite"], [16, "observable-multisite"]], "evolution section": [[9, "evolution-section"]], "correlation section": [[9, "correlation-section"], [15, "correlation-section"], [16, "correlation-section"]], "correlation_length section": [[9, "correlation-length-section"], [15, "correlation-length-section"], [16, "correlation-length-section"]], "File format": [[10, "file-format"]], "Short summary for input files of TeNeS": [[11, "short-summary-for-input-files-of-tenes"]], "Output files": [[13, "output-files"]], "For all modes": [[13, "for-all-modes"]], "parameters.dat": [[13, "parameters-dat"]], "time.dat": [[13, "time-dat"]], "For ground state calculation mode": [[13, "for-ground-state-calculation-mode"]], "density.dat": [[13, "density-dat"]], "onesite_obs.dat": [[13, "onesite-obs-dat"]], "twosite_obs.dat": [[13, "twosite-obs-dat"]], "multisite_obs_#.dat": [[13, "multisite-obs-dat"]], "correlation.dat": [[13, "correlation-dat"]], "correlation_length.dat": [[13, "correlation-length-dat"]], "For time evolution mode": [[13, "for-time-evolution-mode"]], "TE_density.dat": [[13, "te-density-dat"]], "TE_onesite_obs.dat": [[13, "te-onesite-obs-dat"]], "TE_twosite_obs.dat": [[13, "te-twosite-obs-dat"]], "TE_multisite_obs_#.dat": [[13, "te-multisite-obs-dat"]], "TE_correlation.dat": [[13, "te-correlation-dat"]], "TE_correlation_length.dat": [[13, "te-correlation-length-dat"]], "For finite temperature calculation mode": [[13, "for-finite-temperature-calculation-mode"]], "Input file for tenes_simple": [[15, "input-file-for-tenes-simple"]], "model section": [[15, "model-section"]], "Spin system: \"spin\"": [[15, "spin-system-spin"]], "Bosonic system: \"boson\"": [[15, "bosonic-system-boson"]], "lattice section": [[15, "lattice-section"]], "Square lattice": [[15, "square-lattice"]], "Triangular lattice": [[15, "triangular-lattice"]], "Honeycomb lattice": [[15, "honeycomb-lattice"]], "Kagome lattice": [[15, "kagome-lattice"]], "Input file for tenes_std": [[16, "input-file-for-tenes-std"]], "hamiltonian section": [[16, "hamiltonian-section"]], "Usage of tenes": [[18, "usage-of-tenes"]], "Usage": [[19, "usage"]], "Usage of tenes_simple": [[20, "usage-of-tenes-simple"]], "Usage of tenes_std": [[21, "usage-of-tenes-std"]], "Welcome to TeNeS\u2019s documentation!": [[22, "welcome-to-tenes-s-documentation"]], "Contents": [[22, "contents"]], "Indices and tables": [[22, "indices-and-tables"]], "Install": [[23, "install"], [23, "id1"]], "Download": [[23, "download"]], "Prerequisites": [[23, "prerequisites"]], "Parallel Build": [[23, null]], "Disable MPI/ScaLAPACK parallelization": [[23, null]], "Specify compiler": [[23, null]], "Specify ScaLAPACK": [[23, null]], "Use the pre-built mptensor": [[23, null]], "Specify Python interpreter": [[23, null]], "Tutorial": [[24, "tutorial"]], "Ising model with transverse magnetic field": [[25, "ising-model-with-transverse-magnetic-field"]], "Magnetization process of the Heisenberg model on triangular and square lattices": [[26, "magnetization-process-of-the-heisenberg-model-on-triangular-and-square-lattices"]], "Phase diagram of the hardcore boson model on a trianglar lattice": [[27, "phase-diagram-of-the-hardcore-boson-model-on-a-trianglar-lattice"]], "Real-Time Evolution of the Transverse Field Ising Model": [[28, "real-time-evolution-of-the-transverse-field-ising-model"]], "Finite Temperature Calculations for the Transverse Field Ising Model": [[29, "finite-temperature-calculations-for-the-transverse-field-ising-model"]], "Definition of lattices, models, and operators using the standard mode": [[30, "definition-of-lattices-models-and-operators-using-the-standard-mode"]], "Definition of unit cell": [[30, "definition-of-unit-cell"]], "Definition of model (Hamiltonian)": [[30, "definition-of-model-hamiltonian"]], "Bond Hamiltonian": [[30, "bond-hamiltonian"]], "Site Hamiltonian": [[30, "site-hamiltonian"]], "Definition of operators": [[30, "definition-of-operators"]], "Example: Antiferromagnetic Heisenberg model in staggered field": [[30, "example-antiferromagnetic-heisenberg-model-in-staggered-field"]]}, "indexentries": {}}) \ No newline at end of file diff --git a/manual/develop/en/html/tutorial/index.html b/manual/develop/en/html/tutorial/index.html index 93b880b0..9b992f4f 100644 --- a/manual/develop/en/html/tutorial/index.html +++ b/manual/develop/en/html/tutorial/index.html @@ -36,13 +36,15 @@

      4. Tutorial diff --git a/manual/develop/en/html/tutorial/simple_tutorial-5.html b/manual/develop/en/html/tutorial/simple_tutorial-5.html index c88aa3ff..e252273a 100644 --- a/manual/develop/en/html/tutorial/simple_tutorial-5.html +++ b/manual/develop/en/html/tutorial/simple_tutorial-5.html @@ -5,7 +5,7 @@ - 4.2. Magnetization process of the Heisenberg model on triangular and square lattices — TeNeS 1.4-dev documentation + 4.4. Magnetization process of the Heisenberg model on triangular and square lattices — TeNeS 1.4-dev documentation @@ -14,8 +14,8 @@ - - + + @@ -33,7 +33,7 @@
      -

      4.2. Magnetization process of the Heisenberg model on triangular and square lattices

      +

      4.4. Magnetization process of the Heisenberg model on triangular and square lattices

      Next, we introduce the calculation of the magnetization process of the quantum Heisenberg model with spin \(S = 1/2\) defined on a triangular lattice. The Hamiltonian looks like this:

      @@ -177,12 +177,12 @@

      4.2. Magnetization process of the Heisen

      to obtain the magnetization curve as shown in the right panel of -Fig. 4.2. In a similar way,

      +Fig. 4.5. In a similar way,

      load 'plot_ene.gp'

      we obtain the ground-state energy as shown in the left panel of -Fig. 4.2 .

      +Fig. 4.5 .

      As can be seen from the result for a sufficiently large number of steps (for example, 2000 steps), a plateau structure occurs in the magnetization process at the magnetization of \(1/3\) of the @@ -198,7 +198,7 @@

      4.2. Magnetization process of the Heisen
      ../_images/tutorial_5_triangular.png
      -

      Fig. 4.2 Ground state energy (left figure) and magnetization (right figure) of the Heisenberg model on the triangular lattice.

      +

      Fig. 4.5 Ground state energy (left figure) and magnetization (right figure) of the Heisenberg model on the triangular lattice.

      Next, let’s perform the calculation for a model on a square lattice. Use the toml file basic_square.toml and the python script tutorial_magnetization_square.py in the sample/05_magnetization directory. @@ -218,12 +218,12 @@

      4.2. Magnetization process of the Heisen

      Then, the magnetization curve shown in the right panel of -Fig. 4.3 is obtained. In a similar way, by typing the following command,

      +Fig. 4.6 is obtained. In a similar way, by typing the following command,

      load 'plot_ene_square.gp'

      you will obtain the ground-state energy as shown in the left panel of -Fig. 4.3. The calculation is almost converged at 2000 +Fig. 4.6. The calculation is almost converged at 2000 steps, and it can be seen that the plateau structure does not appear unlike the triangular lattice Heisenberg model. Since the energy generally decreases as the number of steps is increased, it is assumed @@ -231,7 +231,7 @@

      4.2. Magnetization process of the Heisen
      ../_images/tutorial_5_square.png
      -

      Fig. 4.3 Ground state energy (left figure) and magnetization (right figure) of the Heisenberg model on the square lattice.

      +

      Fig. 4.6 Ground state energy (left figure) and magnetization (right figure) of the Heisenberg model on the square lattice.

      @@ -264,9 +264,11 @@

      Navigation

    • 3. Usage
    • 4. Tutorial
    • 5. File format
      • @@ -281,8 +283,8 @@

      Related Topics

      diff --git a/manual/develop/en/html/tutorial/simple_tutorial-6.html b/manual/develop/en/html/tutorial/simple_tutorial-6.html index 96b23975..37e35c5c 100644 --- a/manual/develop/en/html/tutorial/simple_tutorial-6.html +++ b/manual/develop/en/html/tutorial/simple_tutorial-6.html @@ -5,7 +5,7 @@ - 4.3. Phase diagram of the hardcore boson model on a trianglar lattice — TeNeS 1.4-dev documentation + 4.5. Phase diagram of the hardcore boson model on a trianglar lattice — TeNeS 1.4-dev documentation @@ -14,8 +14,8 @@ - - + + @@ -33,7 +33,7 @@
      -

      4.3. Phase diagram of the hardcore boson model on a trianglar lattice

      +

      4.5. Phase diagram of the hardcore boson model on a trianglar lattice

      Finally, let us consider a zero-temperature phase diagram of the hardcore boson model on a trianglar lattice. The Hamiltonian of this model is given as

      @@ -43,7 +43,7 @@

      4.3. Phase diagram of the hardcore boson

      where \(\langle i, j\rangle\) indicates a pair of the nearest-neighbor sites, \(\mu\) is a chemical potential, \(t\) is a hopping energy, \(V\) is a strength of the nearest-neighbor interaction. For a hardcore boson system, the maximum number of bosons at each site is restricted to 0 or 1. It is known that several ordered phases characterized by two types of long-range order appear in this model [Wessel] . -One is a solid-like order which exists at a 1/3 filling, where one of three sites is filled in a \(\sqrt{3}\times\sqrt{3}\) ordering with wave vector \(\boldsymbol{Q}=(4\pi/3,0)\) (see the inset of Fig. 4.4 ). +One is a solid-like order which exists at a 1/3 filling, where one of three sites is filled in a \(\sqrt{3}\times\sqrt{3}\) ordering with wave vector \(\boldsymbol{Q}=(4\pi/3,0)\) (see the inset of Fig. 4.7 ). This long-range order is characterized by the structure factor \(S(\boldsymbol{Q})\). The other is a superfluid order which is characterized by the offdiagonal order parameter \(|\langle b \rangle|\).

      To perform calculation for this system, the user can use toml files named basic.toml , nn_obs.toml and a python script file run.py in the direction sample/06_hardcore_boson_triangular . Here, basic.toml specifies the model and its parameters. This file is almost the same as the triangular Heisenberg model described in the previous section and differs from it only in the section model in the last part, where the line type = "boson" specifies the hardcore boson model and t = 0.1 , V = 1 determines the strength of the hopping and nearest-neighbor interaction.

      @@ -92,16 +92,16 @@

      4.3. Phase diagram of the hardcore boson 
      load 'plot.gp'
      -

      Then, we obtain a graph for the structure factor \(S(\boldsymbol{Q})\) and the superfluid order parameter \(|\langle b \rangle|\) as shown in Fig. 4.4 (a). +

      Then, we obtain a graph for the structure factor \(S(\boldsymbol{Q})\) and the superfluid order parameter \(|\langle b \rangle|\) as shown in Fig. 4.7 (a). We note that this calculation is not so accurate because the bond dimension used in the calculation is small. By commenting out the four lines in the beginning of the script run.py , we can perform more accurate calculation at the expense of execution time. -The result is shown in Fig. 4.4 (b). +The result is shown in Fig. 4.7 (b). From these figures, we find that there exists three phases for the ground state, i.e., (a) a superfluid phase (\(-0.5 \lesssim \mu/V \lesssim -0.2\)), (b) a solid phase (\(-0.2 \lesssim \mu/V \lesssim 2.4\)), and (c) a supersolid phase (\(2.4 \lesssim \mu/V\)). This result is consistent with the previous work [Wessel] .

      ../_images/tutorial_6_hardcore_boson.png
      -

      Fig. 4.4 Phase diagram of the hardcore boson model on a triangular lattice. (a) The bond dimension is 2. (b) The bond dimension is 5. Inset: a particle pattern for a solid phase.

      +

      Fig. 4.7 Phase diagram of the hardcore boson model on a triangular lattice. (a) The bond dimension is 2. (b) The bond dimension is 5. Inset: a particle pattern for a solid phase.

      Reference

      @@ -137,9 +137,11 @@

      Navigation

    • 3. Usage
    • 4. Tutorial
    • 5. File format
      • @@ -154,8 +156,8 @@

      Related Topics

      diff --git a/manual/develop/en/html/tutorial/simple_tutorial-7.html b/manual/develop/en/html/tutorial/simple_tutorial-7.html new file mode 100644 index 00000000..3271fba6 --- /dev/null +++ b/manual/develop/en/html/tutorial/simple_tutorial-7.html @@ -0,0 +1,223 @@ + + + + + + + + 4.2. Real-Time Evolution of the Transverse Field Ising Model — TeNeS 1.4-dev documentation + + + + + + + + + + + + + + + + + + + +
      +
      +
      + + +
      + +
      +

      4.2. Real-Time Evolution of the Transverse Field Ising Model

      +

      Here, we introduce a calculation example for the real-time evolution of the Ising model on a square lattice when a transverse magnetic field, denoted by hx, is applied. The input and script files used in this tutorial can be found in sample/07_timeevolution.

      +

      Initially, we compute the ground state (refer to the simple.toml file) which serves as our starting state. Specifically, it’s set as:

      +
      [parameter]
+[parameter.general]
+output = "output"
+tensor_save = "save_tensor"
+
+[parameter.simple_update]
+num_step = 10
+tau = 0.01
+
+[parameter.full_update]
+num_step = 0
+tau = 0.0
+
+[parameter.ctm]
+meanfield_env = true
+iteration_max = 10
+dimension = 10
+
+[lattice]
+type = "square lattice"
+L = 2
+W = 2
+virtual_dim = 3
+initial = "ferro"
+
+[model]
+type = "spin"
+Jz = -1.0
+Jx = 0.0
+Jy = 0.0
+hx = 0.0
+
      +
      +

      Given that Jz = -1.0, the ground state becomes ferromagnetic. We use the ground state as the initial state, and save the state tensor with tensor_save = "save_tensor".

      +

      Next, we prepare the input file for the real-time evolution. This can be achieved by setting the mode to time. Below is a sample input file (simple_te_strong.toml):

      +
      [parameter]
+[parameter.general]
+output = "output_te_strong"
+tensor_load = "save_tensor"
+mode = "time"
+
+[parameter.simple_update]
+num_step = 500
+tau = 0.01
+
+[parameter.full_update]
+num_step = 0
+tau = 0.0
+
+[parameter.ctm]
+meanfield_env = true
+iteration_max = 10
+dimension = 10
+
+[lattice]
+type = "square lattice"
+L = 2
+W = 2
+virtual_dim = 3
+initial = "ferro"
+
+[model]
+type = "spin"
+Jz = -1.0
+Jx = 0.0
+Jy = 0.0
+hx = 2.0
+
      +
      +

      In this case, the transverse field is set to hx = 2.0, and the time-step for evolution is tau = 0.01. Moreover, since we are utilizing the ground state as our initial condition, we load the state tensor with tensor_load = "save_tensor". For observing the time evolution with different transverse magnetic fields, we’ve also prepared sample input files named simple_te_middle.toml and simple_te_weak.toml. Additionally, there’s a script named run.sh to execute these calculations in one go. Ensure that paths to tools like tenes are set correctly, and then execute the calculations with:

      +
      sh run.sh
+
      +
      +

      The computation will conclude in several seconds. Once done, launch gnuplot and enter:

      +
      load 'plot.plt'
+
      +
      +

      This will plot the temporal evolution of magnetization, \(S_z\). The result is displayed in Fig. 4.2.

      +
      +../_images/tutorial_07_timeevolution.png +
      +

      Fig. 4.2 Graph illustrating the real-time evolution of the Ising model. The vertical axis represents magnetization, and the horizontal axis represents time.

      +
      +
      +

      As time evolution progresses, the entanglement increases. At a certain point, the tensor network’s capacity may be insufficient to express the wave function. In our case, the jump at t=4.25 for hx=2.0 indicates this issue. When applying this in practice, ensure no such discontinuities exist. If jumps are observed, steps like increasing the virtual_dimension might be necessary. For instance, adjusting it to virtual_dimension = 10 and redoing the calculation as described above will eliminate the discontinuity, as can be seen in Fig. 4.3.

      +
      +../_images/tutorial_07_timeevolution_D10.png +
      +

      Fig. 4.3 Graph showcasing the real-time evolution of the Ising model. The vertical axis denotes magnetization, while the horizontal axis represents time. Results when virtual_dimension = 10 are applied.

      +
      +
      +
      + + +
      + +
      +
      + +
      +
      +
      + ©2019-, Institute for Solid State Physics, University of Tokyo. + + | + Powered by Sphinx 7.1.2 + & Alabaster 0.7.13 + + | + Page source +
      + + + + + + \ No newline at end of file diff --git a/manual/develop/en/html/tutorial/simple_tutorial-8.html b/manual/develop/en/html/tutorial/simple_tutorial-8.html new file mode 100644 index 00000000..f1efc7f8 --- /dev/null +++ b/manual/develop/en/html/tutorial/simple_tutorial-8.html @@ -0,0 +1,182 @@ + + + + + + + + 4.3. Finite Temperature Calculations for the Transverse Field Ising Model — TeNeS 1.4-dev documentation + + + + + + + + + + + + + + + + + + + +
      +
      +
      + + +
      + +
      +

      4.3. Finite Temperature Calculations for the Transverse Field Ising Model

      +

      In this section, we present a calculation example of the ferromagnetic Ising model on a square lattice subjected to a transverse magnetic field, denoted by hx, at finite temperatures. The input and script files used in this tutorial are located in the sample/08_finitetemperature directory. Below is a sample input file (simple_ft_strong.toml):

      +
      [parameter]
+[parameter.general]
+mode = "finite"
+is_real = false
+output = "output_ft_strong"
+measure_interval = [10, 10, 5]
+
+[parameter.simple_update]
+num_step = [50, 200, 10]
+tau = [0.01, 0.005, 0.05]
+
+[parameter.full_update]
+num_step = 0
+tau = 0.0
+
+[parameter.ctm]
+iteration_max = 10
+dimension = 10
+
+[lattice]
+type = "square lattice"
+L = 2
+W = 2
+virtual_dim = 3
+
+[model]
+type = "spin"
+Jz = -1.0
+Jx = 0.0
+Jy = 0.0
+hx = 2.0
+
      +
      +

      To perform finite temperature calculations, set the mode to finite. Here, the transverse magnetic field is set to hx = 2.0 with tau = 0.01 (the inverse temperature step size is 2 times tau). To observe the behavior at different transverse magnetic fields, we’ve provided additional sample input files: simple_ft_middle.toml, simple_te_weak.toml, and simple_ft_zero.toml. Moreover, a script named run.sh has been set up to execute all these calculations simultaneously. Ensure you’ve added tools like tenes to your PATH, then initiate the calculations with:

      +
      sh run.sh
+
      +
      +

      The computation should complete in about a minute. To visualize the results, scripts have been prepared to plot energy, heat capacity, and magnetization (\(S_x\), \(S_z\)): plot_e.plt, plot_c.plt, plot_mx.plt, and plot_mz.plt. Running the following:

      +
      gnuplot -persist plot_e.plt
+gnuplot -persist plot_c.plt
+gnuplot -persist plot_mx.plt
+gnuplot -persist plot_mz.plt
+
      +
      +

      will display plots for energy, heat capacity, and magnetizations (\(S_x\) and \(S_z\)). The resulting plots are illustrated in Fig. 4.4. For comparison, results obtained using Quantum Monte Carlo calculations are also shown (using ALPS/looper).

      +
      +../_images/tutorial_08_finitetemperature.png +
      +

      Fig. 4.4 Graphs for the finite temperature calculations of the Ising model: (a) energy, (b) heat capacity, (c) \(S_x\), and (d) \(S_z\). The vertical axis represents the physical quantity, and the horizontal axis denotes temperature.

      +
      +
      +
      + + +
      + +
      +
      + +
      +
      +
      + ©2019-, Institute for Solid State Physics, University of Tokyo. + + | + Powered by Sphinx 7.1.2 + & Alabaster 0.7.13 + + | + Page source +
      + + + + + + \ No newline at end of file diff --git a/manual/develop/en/html/tutorial/standard_tutorial-1.html b/manual/develop/en/html/tutorial/standard_tutorial-1.html index 27586ff2..993ace1a 100644 --- a/manual/develop/en/html/tutorial/standard_tutorial-1.html +++ b/manual/develop/en/html/tutorial/standard_tutorial-1.html @@ -5,7 +5,7 @@ - 4.4. Definition of lattices, models, and operators using the standard mode — TeNeS 1.4-dev documentation + 4.6. Definition of lattices, models, and operators using the standard mode — TeNeS 1.4-dev documentation @@ -15,7 +15,7 @@ - + @@ -33,15 +33,15 @@
      -

      4.4. Definition of lattices, models, and operators using the standard mode

      +

      4.6. Definition of lattices, models, and operators using the standard mode

      By using the standard mode, users can define own lattices, models, and operators. In this section, we explain how to use the standard mode.

      -

      4.4.1. Definition of unit cell

      +

      4.6.1. Definition of unit cell

      ../_images/en_tutorial_1_Tensor.png
      -

      Fig. 4.5 [tensor] and [[tensor.unitcell]]

      +

      Fig. 4.8 [tensor] and [[tensor.unitcell]]

      Unit cells are defined using [tensor] and [[tensor.unitcell]]:

      @@ -64,11 +64,11 @@

      4.4.1. Definition of unit cell -

      4.4.2. Definition of model (Hamiltonian)

      +

      4.6.2. Definition of model (Hamiltonian)

      ../_images/en_tutorial_1_Hamiltonian.png
      -

      Fig. 4.6 [[hamiltonian]]

      +

      Fig. 4.9 [[hamiltonian]]

      TeNeS treats the Hamiltonian as the sum of bond Hamiltonians (two-site Hamiltonians) and site Hamiltonians (one-site Hamiltonians).

      @@ -136,11 +136,11 @@

      Site Hamiltonian -

      4.4.3. Definition of operators

      +

      4.6.3. Definition of operators

      ../_images/en_tutorial_1_Observable.png
      -

      Fig. 4.7 [[observable.onesite]]

      +

      Fig. 4.10 [[observable.onesite]]

      Operators whose expected values are finally computed are defined in [observable]. @@ -195,7 +195,7 @@

      4.4.3. Definition of operatorsops can be used to specify them.

      -

      4.4.4. Example: Antiferromagnetic Heisenberg model in staggered field

      +

      4.6.4. Example: Antiferromagnetic Heisenberg model in staggered field

      Let us consider the antiferromagnetic Heisenberg model in staggered field. The Hamiltonian is as follows

      @@ -373,9 +373,11 @@

      Navigation

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      • @@ -390,7 +392,7 @@

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