Add example for Heisenberg AFM

Author: JanLuca

examples/heisenberg_afm_square.py

@@ -0,0 +1,110 @@
+import varipeps
+import jax
+import jax.numpy as jnp
+
+# Config Setting
+## Set maximal steps for the CTMRG routine
+varipeps.config.ad_custom_max_steps = 100
+## Set maximal steps for the fix point routine in the gradient calculation
+varipeps.config.ctmrg_max_steps = 100
+## Set convergence threshold for the CTMRG routine
+varipeps.config.ctmrg_convergence_eps = 1e-7
+## Set convergence threshold for the fix point routine in the gradient calculation
+varipeps.config.ad_custom_convergence_eps = 5e-8
+## Enable/Disable printing of the convergence of the single CTMRG/gradient fix point steps.
+## Useful to enable this during debugging, should be disabled for batch runs
+varipeps.config.config.ctmrg_print_steps = True
+varipeps.config.config.ad_custom_print_steps = False
+## Select the method used to calculate the descent direction during optimization
+varipeps.config.config.optimizer_method = varipeps.config.Optimizing_Methods.CG
+## Select the method used to calculate the (full) projectors in the CTMRG routine
+varipeps.config.config.ctmrg_full_projector_method = (
+    varipeps.config.Projector_Method.FISHMAN
+)
+## Set maximal steps for the optimization routine
+varipeps.config.config.optimizer_max_steps = 2000
+## Increase enviroment bond dimension if truncation error is below this value
+varipeps.config.config.ctmrg_heuristic_increase_chi_threshold = 1e-4
+
+# Set constants for the simulation
+modelName = "HeisenbergModel"
+# Interaction strength
+J = 1
+# iPEPS bond dimension
+chiB = 2
+# Physical dimension
+p = 2
+# Maximal enviroment bond dimension
+maxChi = 36
+# Start value for enviroment bond dimension
+startChi = chiB**2 if chiB**2 < maxChi else maxChi
+
+# Unit cell structure
+structure = [[0, 1], [1, 0]]
+
+# define spin-1/2 matrices
+Id = jnp.eye(2)
+Sx = jnp.array([[0, 1], [1, 0]]) / 2
+Sy = jnp.array([[0, -1j], [1j, 0]]) / 2
+Sz = jnp.array([[1, 0], [0, -1]]) / 2
+
+# construct Hamiltonian terms
+hamiltonianGates = J * (jnp.kron(Sx, Sx) + jnp.kron(Sy, Sy) + jnp.kron(Sz, Sz))
+
+# create function to compute expectation values for the square Heisenberg AFM
+exp_func = varipeps.expectation.Two_Sites_Expectation_Value(
+    horizontal_gates=(hamiltonianGates,),
+    vertical_gates=(hamiltonianGates,),
+)
+
+# Create random initialization for the iPEPS unit cell
+unitcell = varipeps.peps.PEPS_Unit_Cell.random(
+    structure,  # Unit cell structure
+    p,  # Physical dimension
+    chiB,  # iPEPS bond dimension
+    startChi,  # Start value for enviroment bond dimension
+    float,  # Data type for the tensors: float (real) or complex tensors
+    max_chi=maxChi,  # Maximal enviroment bond dimension
+)
+
+# Run optimization
+result = varipeps.optimization.optimize_peps_network(
+    unitcell,
+    exp_func,
+    autosave_filename=f"data/autosave_square_chiB_{chiB:d}.hdf5",
+)
+
+# Calculate magnetic expectation values
+Mag_Gates = [Sx, Sy, Sz]
+
+
+def calc_magnetic(unitcell):
+    mag_result = []
+    for ti, t in enumerate(unitcell.get_unique_tensors()):
+        r = varipeps.expectation.one_site.calc_one_site_multi_gates(
+            t.tensor, t, Mag_Gates
+        )
+        mag_result += r
+    return mag_result
+
+
+magnetic_exp_values = calc_magnetic(result.unitcell)
+
+# Define some auxiliary data which should be stored along the final iPEPS unit cell
+auxiliary_data = {
+    "best_energy": result.fun,
+    "best_run": result.best_run,
+    "magnetic_exp_values": magnetic_exp_values,
+}
+for k in sorted(result.max_trunc_error_list.keys()):
+    auxiliary_data[f"max_trunc_error_list_{k:d}"] = result.max_trunc_error_list[k]
+    auxiliary_data[f"step_energies_{k:d}"] = result.step_energies[k]
+    auxiliary_data[f"step_chi_{k:d}"] = result.step_chi[k]
+    auxiliary_data[f"step_conv_{k:d}"] = result.step_conv[k]
+    auxiliary_data[f"step_runtime_{k:d}"] = result.step_runtime[k]
+
+# save full iPEPS state
+result.unitcell.save_to_file(
+    f"data/heisenberg_square_J_{J:d}_chiB_{chiB:d}_chiMax_{chiM:d}.hdf5",
+    auxiliary_data=auxiliary_data,
+)