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isotns.py
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isotns.py
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import numpy as np
from misc import *
from tebd import tebd, get_time_evol
from moses_move import *
""" Base class for isometric tensor network states. The primary method is
full_sweep(), which performs a series of sweeps and rotations around the peps.
Each sweep corresponds to a series of TEBD and moses_moves across the peps in
it's current orientation. For more details, see
https://arxiv.org/pdf/1902.05100.pdf.
The PEPS index convention is
4
|
1---T---2
/|
0 3
The PEPS is stored as a list of lists of these tensors. PEPS[x] should
give a column.
This code is written to exactly match Mike and Frank's... keep in mind
that np vs sp do introduce numerical errors.
"""
class isotns:
""" Base class for isotns.
Parameters
----------
peps: List of lists of numpy arrays, representing a peps.
tebd_params: Dictionary of tebd params. Format
{trunc_params: {chi_max = chi_max, p_trunc = p_trunc,
moses_trunc_params: {chiV_max, chiH_max,
etaV_max, etaH_max}
}
}
Should contain subdictionary
trunc_params (which must have p_trunc and chi_max, and can optionally
contain moses_move truncation_params)
Attributes
----------
peps: List of lists of tensors making up the peps.
Lx: Length in x direction.
Ly: Length in y direction.
Ss: List of lists of dimension (Lx - 1, Ly - 1). Each element is the
entanglement entropy across a bond (I don't know if this actually is valid).
"""
def __init__(self, peps, trunc_params):
self.peps = peps
self.Lx = len(peps)
self.Ly = len(peps[0])
self.tp = trunc_params
def rotate(self):
""" Rotates a peps counter clockwise by 90 degrees. """
peps = self.peps
Lx, Ly = self.Lx, self.Ly
rpeps = [[None] * Lx for i in range(Ly)] # Rotated dimensions
for x in range(Lx):
for y in range(Ly):
#rpeps[y][Lx - 1 - x] = rotate_CC(peps[x][y]).copy()
# TODO figure out why this is right...
rpeps[y][x] = rotate_CC(peps[x][Ly - 1 - y]).copy()
self.peps = rpeps
def sweep_with_rotation(self, Us, trunc_params, Os = None):
""" Performs a series of 4 peps_sweep()s. Between each sweep, rotates the
peps by 90 degrees CC. In this way, we perform TEBD on all rows and columns.
Parameters
----------
peps: Ly x Lx list of lists of tensors.
Us: List of 4 lists, one for each sweep direction.
trunc_params: truncation_params
Os: List of 4 lists, one for each sweep direction.
Returns
----------
peps: Time evolved peps
info: Dictionary of information about the peps.
"""
info = dict(expectation_O = [],
tebd_err = [0.0] * 4,
moses_err = [0.0] * 4
)
if Us is None:
Us = [None] * 4
if Os is None:
Os = [None] * 4
for i in range(4):
print("Starting sequence {i} of full sweep".format(i=i))
info_ = self._full_sweep(Us[i], Os[i])
info["expectation_O"].append(info_["expectation_O"])
info["tebd_err"][i] += np.sum(info_["tebd_err"])
info["moses_err"][i] += np.sum(info_["tebd_err"])
self.rotate()
return(info)
def tebd2(self, Hs, dt, trunc_params, Nsteps = None, min_dE = None):
""" Performs tebd2 ith second order Trotterization.
Parameters
----------
Hs: List of vertical and horizontal Hamiltonians (NOT time
evolution operator)
dt: Time interval.
trunc_params: truncation param dict
Nsteps: Number of full sweeps with rotations across peps (i.e.,
four sweeps back and forth).
min_dE: Break after the change in energy between sweeps is less than min_dE.
Returns
---------
info: Dict on final run
"""
if min_dE is None:
min_dE = np.float("inf")
if Nsteps is None:
Nsteps = np.float("inf")
Uv = get_time_evol(Hs[0], dt)
Uh = get_time_evol(Hs[1], dt)
Uv2 = get_time_evol(Hs[0], dt / 2.) # Second order Trotter
info = self.sweep_with_rotation([Uv2, Uh, Uv, Uh], trunc_params,
Os=[None, None, None, Hs[1]])
E_curr = np.sum(info["expectation_O"][3])
step = 0
dE = np.float("inf")
while step < Nsteps and np.abs(dE) < min_dE:
if step % 10 == 0:
print("Step {0}".format(step))
info = self.sweep_with_rotation([Uv, Uh, Uv, Uh], trunc_params,
Os = [None, None, None, Hs[1]])
E_prev = E_curr
E_curr = np.sum(info["expectation_O"][3])
dE = E_curr - E_prev
step += 1
info = self.sweep_with_rotation([Uv2, None, None, None],
trunc_params,
Os=[None, None, Hs[0], Hs[1]])
return(info)
def _full_sweep(self, U, O = None):
Psi = self.peps[0]
Lx = self.Lx
Ly = self.Ly
trunc_params = self.tp
tebd_2_mm_trunc = 0.1 # IDK what this is...
min_p_trunc = self.tp["p_trunc"]
# This is adjusted according to the errors. Not sure why exactly
target_p_trunc = min_p_trunc
info = dict(expectation_O = [],
tebd_err = [],
moses_err = [],
moses_d_err = [],
nrm = 1.)
if U is None:
U = [None]
if O is None:
O = [None]
for j in range(Lx):
tebd_trunc_params = dict(p_trunc = target_p_trunc,
chi_max = trunc_params["chi_max"])
Psi, tebd_info = tebd(Psi, U,
O,
tebd_trunc_params, direct = "L")
info["expectation_O"].append(tebd_info['expectation_O'])
info["tebd_err"].append(tebd_info['tebd_err'])
info["nrm"] *= tebd_info["nrm"]
if j < Lx - 1:
Psi, pipe = mps_group_legs(Psi, [[0,1],[2]])
A, Lambda, moses_info = moses_move(Psi, trunc_params)
info["moses_err"].append(moses_info.setdefault("error", np.nan))
info["moses_d_err"].append(moses_info.setdefault("d_error", np.nan))
if not np.isnan(info["moses_err"][-1]):
target_p_trunc = np.max([tebd_2_mm_trunc * info['moses_err'][-1] /\
len(Psi), min_p_trunc])
A = mps_ungroup_legs(A, pipe)
self.peps[j] = A
Psi, pipe = mps_group_legs(self.peps[j + 1], axes=[[1],[0,2]])
self.peps[j + 1] = Psi
Psi = contract_mpos(Lambda, Psi)
Psi = mps_ungroup_legs(Psi, pipe)
else:
Psi = canonical_form(Psi, form='A')
self.peps[j] = Psi
return(info)
# Static methods
def rotate_CC(T):
""" Rotates a tensor T counter clockwise """
if T.ndim != 5:
raise ValueError("T should have 5 legs")
return(T.transpose([0,4,3,1,2]))