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6288873 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 | 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.ctmrg_print_steps = True
varipeps.config.ad_custom_print_steps = False
## Select the method used to calculate the descent direction during optimization
varipeps.config.optimizer_method = varipeps.config.Optimizing_Methods.L_BFGS
## Select the method used to calculate the (full) projectors in the CTMRG routine
varipeps.config.ctmrg_full_projector_method = varipeps.config.Projector_Method.FISHMAN
## Set maximal steps for the optimization routine
varipeps.config.optimizer_max_steps = 2000
## Increase enviroment bond dimension if truncation error is below this value
varipeps.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 = 64
# Start value for enviroment bond dimension
startChi = maxChi
# 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.triangular_two_sites.Triangular_Two_Sites_Expectation_Value(
horizontal_gates=(hamiltonianGates,),
vertical_gates=(hamiltonianGates,),
diagonal_gates=(hamiltonianGates,),
real_d=p,
is_spiral_peps=True,
spiral_unitary_operator=Sy,
)
)
# Unit cell structure
structure = [[0]]
# 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
peps_type=varipeps.peps.PEPS_Type.TRIANGULAR, # Select triangular PEPS
)
# Run optimization
result = varipeps.optimization.optimize_unitcell_fixed_spiral_vector(
unitcell,
jnp.array((2 / 3, 2 / 3), dtype=jnp.float64), # Spiral vector
exp_func,
autosave_filename=f"data/autosave_triangular_chiB_{chiB:d}_chiMax_{maxChi: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.triangular_one_site.calc_triangular_one_site(
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_triangular_J_{J:d}_chiB_{chiB:d}_chiMax_{maxChi:d}.hdf5",
auxiliary_data=auxiliary_data,
)
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