Deploy docs to develop by GitHub Actions triggered by e2f21a1

manual/develop/en/html/_sources/tutorial/index.rst.txt

@@ -7,6 +7,8 @@ Tutorial
    :maxdepth: 2
 
    simple_tutorial-1
+   simple_tutorial-7
+   simple_tutorial-8
    simple_tutorial-5
    simple_tutorial-6
-   standard_tutorial-1
+   standard_tutorial-1

manual/develop/en/html/_sources/tutorial/simple_tutorial-7.rst.txt

@@ -0,0 +1,44 @@
+.. highlight:: none
+
+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:
+
+.. literalinclude:: ../../../../sample/07_timeevolution/simple.toml
+
+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``):
+
+.. literalinclude:: ../../../../sample/07_timeevolution/simple_te_strong.toml
+
+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, :math:`S_z`. The result is displayed in :numref:`fig_tutorial7_timeevolution`.
+
+.. figure:: ../../img/tutorial_07_timeevolution.*
+    :name: fig_tutorial7_timeevolution
+    :width: 600px
+
+    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 :numref:`fig_tutorial7_te_D10`.
+
+.. figure:: ../../img/tutorial_07_timeevolution_D10.*
+    :name: fig_tutorial7_te_D10
+    :width: 600px
+
+    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.

manual/develop/en/html/_sources/tutorial/simple_tutorial-8.rst.txt

@@ -0,0 +1,31 @@
+.. highlight:: none
+
+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`):
+
+.. literalinclude:: ../../../../sample/08_finitetemperature/simple_ft_strong.toml
+
+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 (:math:`S_x`, :math:`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 (:math:`S_x` and :math:`S_z`). The resulting plots are illustrated in :numref:`fig_tutorial8_finitetemperature`. For comparison, results obtained using Quantum Monte Carlo calculations are also shown (using ``ALPS/looper``).
+
+.. figure:: ../../img/tutorial_08_finitetemperature.*
+    :name: fig_tutorial8_finitetemperature
+    :width: 600px
+
+    Graphs for the finite temperature calculations of the Ising model: (a) energy, (b) heat capacity, (c) :math:`S_x`, and (d) :math:`S_z`. The vertical axis represents the physical quantity, and the horizontal axis denotes temperature.

manual/develop/en/html/file_specification/index.html

@@ -14,7 +14,7 @@
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
     <link rel="next" title="5.1. Short summary for input files of TeNeS" href="input_summary.html" />
-    <link rel="prev" title="4.4. Definition of lattices, models, and operators using the standard mode" href="../tutorial/standard_tutorial-1.html" />
+    <link rel="prev" title="4.6. Definition of lattices, models, and operators using the standard mode" href="../tutorial/standard_tutorial-1.html" />
 
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
 
@@ -118,7 +118,7 @@ <h3>Navigation</h3>
 <h3>Related Topics</h3>
 <ul>
   <li><a href="../index.html">Documentation overview</a><ul>
-      <li>Previous: <a href="../tutorial/standard_tutorial-1.html" title="previous chapter"><span class="section-number">4.4. </span>Definition of lattices, models, and operators using the standard mode</a></li>
+      <li>Previous: <a href="../tutorial/standard_tutorial-1.html" title="previous chapter"><span class="section-number">4.6. </span>Definition of lattices, models, and operators using the standard mode</a></li>
       <li>Next: <a href="input_summary.html" title="next chapter"><span class="section-number">5.1. </span>Short summary for input files of TeNeS</a></li>
   </ul></li>
 </ul>

manual/develop/en/html/index.html

@@ -59,9 +59,11 @@ <h2>Contents<a class="headerlink" href="#contents" title="Permalink to this head
 </li>
 <li class="toctree-l1"><a class="reference internal" href="tutorial/index.html">4. Tutorial</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="tutorial/simple_tutorial-1.html">4.1. Ising model with transverse magnetic field</a></li>
-<li class="toctree-l2"><a class="reference internal" href="tutorial/simple_tutorial-5.html">4.2. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
-<li class="toctree-l2"><a class="reference internal" href="tutorial/simple_tutorial-6.html">4.3. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
-<li class="toctree-l2"><a class="reference internal" href="tutorial/standard_tutorial-1.html">4.4. Definition of lattices, models, and operators using the standard mode</a></li>
+<li class="toctree-l2"><a class="reference internal" href="tutorial/simple_tutorial-7.html">4.2. Real-Time Evolution of the Transverse Field Ising Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="tutorial/simple_tutorial-8.html">4.3. Finite Temperature Calculations for the Transverse Field Ising Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="tutorial/simple_tutorial-5.html">4.4. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
+<li class="toctree-l2"><a class="reference internal" href="tutorial/simple_tutorial-6.html">4.5. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
+<li class="toctree-l2"><a class="reference internal" href="tutorial/standard_tutorial-1.html">4.6. Definition of lattices, models, and operators using the standard mode</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="file_specification/index.html">5. File format</a><ul>

manual/develop/en/html/tutorial/index.html

@@ -36,13 +36,15 @@ <h1><span class="section-number">4. </span>Tutorial<a class="headerlink" href="#
 <div class="toctree-wrapper compound">
 <ul>
 <li class="toctree-l1"><a class="reference internal" href="simple_tutorial-1.html">4.1. Ising model with transverse magnetic field</a></li>
-<li class="toctree-l1"><a class="reference internal" href="simple_tutorial-5.html">4.2. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
-<li class="toctree-l1"><a class="reference internal" href="simple_tutorial-6.html">4.3. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
-<li class="toctree-l1"><a class="reference internal" href="standard_tutorial-1.html">4.4. Definition of lattices, models, and operators using the standard mode</a><ul>
-<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#definition-of-unit-cell">4.4.1. Definition of unit cell</a></li>
-<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#definition-of-model-hamiltonian">4.4.2. Definition of model (Hamiltonian)</a></li>
-<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#definition-of-operators">4.4.3. Definition of operators</a></li>
-<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#example-antiferromagnetic-heisenberg-model-in-staggered-field">4.4.4. Example: Antiferromagnetic Heisenberg model in staggered field</a></li>
+<li class="toctree-l1"><a class="reference internal" href="simple_tutorial-7.html">4.2. Real-Time Evolution of the Transverse Field Ising Model</a></li>
+<li class="toctree-l1"><a class="reference internal" href="simple_tutorial-8.html">4.3. Finite Temperature Calculations for the Transverse Field Ising Model</a></li>
+<li class="toctree-l1"><a class="reference internal" href="simple_tutorial-5.html">4.4. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
+<li class="toctree-l1"><a class="reference internal" href="simple_tutorial-6.html">4.5. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
+<li class="toctree-l1"><a class="reference internal" href="standard_tutorial-1.html">4.6. Definition of lattices, models, and operators using the standard mode</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#definition-of-unit-cell">4.6.1. Definition of unit cell</a></li>
+<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#definition-of-model-hamiltonian">4.6.2. Definition of model (Hamiltonian)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#definition-of-operators">4.6.3. Definition of operators</a></li>
+<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html#example-antiferromagnetic-heisenberg-model-in-staggered-field">4.6.4. Example: Antiferromagnetic Heisenberg model in staggered field</a></li>
 </ul>
 </li>
 </ul>
@@ -77,9 +79,11 @@ <h3>Navigation</h3>
 <li class="toctree-l1"><a class="reference internal" href="../how_to_use/index.html">3. Usage</a></li>
 <li class="toctree-l1 current"><a class="current reference internal" href="#">4. Tutorial</a><ul>
 <li class="toctree-l2"><a class="reference internal" href="simple_tutorial-1.html">4.1. Ising model with transverse magnetic field</a></li>
-<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-5.html">4.2. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
-<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-6.html">4.3. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
-<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html">4.4. Definition of lattices, models, and operators using the standard mode</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-7.html">4.2. Real-Time Evolution of the Transverse Field Ising Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-8.html">4.3. Finite Temperature Calculations for the Transverse Field Ising Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-5.html">4.4. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-6.html">4.5. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
+<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html">4.6. Definition of lattices, models, and operators using the standard mode</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../file_specification/index.html">5. File format</a></li>

manual/develop/en/html/tutorial/simple_tutorial-1.html

@@ -13,7 +13,7 @@
     <script src="../_static/sphinx_highlight.js?v=4825356b"></script>
     <link rel="index" title="Index" href="../genindex.html" />
     <link rel="search" title="Search" href="../search.html" />
-    <link rel="next" title="4.2. Magnetization process of the Heisenberg model on triangular and square lattices" href="simple_tutorial-5.html" />
+    <link rel="next" title="4.2. Real-Time Evolution of the Transverse Field Ising Model" href="simple_tutorial-7.html" />
     <link rel="prev" title="4. Tutorial" href="index.html" />
 
   <link rel="stylesheet" href="../_static/custom.css" type="text/css" />
@@ -248,9 +248,11 @@ <h3>Navigation</h3>
 <li class="toctree-l1"><a class="reference internal" href="../how_to_use/index.html">3. Usage</a></li>
 <li class="toctree-l1 current"><a class="reference internal" href="index.html">4. Tutorial</a><ul class="current">
 <li class="toctree-l2 current"><a class="current reference internal" href="#">4.1. Ising model with transverse magnetic field</a></li>
-<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-5.html">4.2. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
-<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-6.html">4.3. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
-<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html">4.4. Definition of lattices, models, and operators using the standard mode</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-7.html">4.2. Real-Time Evolution of the Transverse Field Ising Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-8.html">4.3. Finite Temperature Calculations for the Transverse Field Ising Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-5.html">4.4. Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
+<li class="toctree-l2"><a class="reference internal" href="simple_tutorial-6.html">4.5. Phase diagram of the hardcore boson model on a trianglar lattice</a></li>
+<li class="toctree-l2"><a class="reference internal" href="standard_tutorial-1.html">4.6. Definition of lattices, models, and operators using the standard mode</a></li>
 </ul>
 </li>
 <li class="toctree-l1"><a class="reference internal" href="../file_specification/index.html">5. File format</a></li>
@@ -266,7 +268,7 @@ <h3>Related Topics</h3>
   <li><a href="../index.html">Documentation overview</a><ul>
   <li><a href="index.html"><span class="section-number">4. </span>Tutorial</a><ul>
       <li>Previous: <a href="index.html" title="previous chapter"><span class="section-number">4. </span>Tutorial</a></li>
-      <li>Next: <a href="simple_tutorial-5.html" title="next chapter"><span class="section-number">4.2. </span>Magnetization process of the Heisenberg model on triangular and square lattices</a></li>
+      <li>Next: <a href="simple_tutorial-7.html" title="next chapter"><span class="section-number">4.2. </span>Real-Time Evolution of the Transverse Field Ising Model</a></li>
   </ul></li>
   </ul></li>
 </ul>