def excitation_density_sq(self):
# Get the number of sites
num_sites = self.num_sites
# Define local operators
I = np.zeros((1, 2, 2, 1))
I[0, :, :, 0] = np.identity(2)
n = np.zeros((1, 2, 2, 1))
n[0, :, :, 0] = np.array([[0, 0], [0, 1]])
# Set the excitation to zero
excitation = 0
# Loop through each site
for site in range(num_sites):
# Construct an MPO with n at site and I everywhere else
MPO = mp.mpo(2, num_sites, 1, I)
MPO.edit_structure(site, n)
# Find the expection wrt psi
excitation += mp.expectation(MPO, self.psi)**2
# Divide by the number of sites
excitation = excitation / num_sites
# Return excitation
return excitation
def correlation(MPS, distance=1):
# Get the number of sites
sites = MPS.length
# Operators
I = np.array([[1, 0], [0, 1]])
n = np.array([[0, 0], [0, 1]])
# Find the amount of pairs
pairs = sites - distance
# Store correlation
correlation = 0
# Loop through each pair
for site in range(pairs):
# Create an MPO
local = np.zeros((1, 2, 2, 1))
local[0, :, :, 0] = I
mpo = mp.mpo(2, sites, 1, local)
# Add the n operator to the correct sites
nlocal = np.zeros((1, 2, 2, 1))
nlocal[0, :, :, 0] = n
mpo.edit_structure(site, nlocal)
mpo.edit_structure(site + distance, nlocal)
# Calculate the expectation
correlation += mp.expectation(mpo, MPS)
return correlation / pairs
def excitation(MPS):
#Get the number of sites
sites = MPS.length
# Create the MPO
I = np.array([[1, 0], [0, 1]])
n = np.array([[0, 0], [0, 1]])
local = np.zeros((2, 2, 2, 2))
local[0, :, :, 0] = I
local[1, :, :, 0] = n
local[1, :, :, 1] = I
ni = mp.mpo(2, sites, 2, local)
# Calculate excitation
excitation = mp.expectation(ni, MPS) / sites
return excitation / mp.dot(MPS, MPS)
def occupation(MPS):
# Get the number of sites
sites = MPS.length
# Store occupations
occupations = np.zeros(sites)
# Loop through each site
for site in range(sites):
# Create the MPO
I = np.array([[1, 0], [0, 1]])
n = np.array([[0, 0], [0, 1]])
local = np.zeros((1, 2, 2, 1))
local[0, :, :, 0] = I
ni = mp.mpo(2, sites, 1, local)
nlocal = np.zeros((1, 2, 2, 1))
nlocal[0, :, :, 0] = n
ni.edit_structure(site, nlocal)
# Calculate occupation
occupations[site] = mp.expectation(ni, MPS)
return occupations / mp.dot(MPS, MPS)
def __init__(self, N, c, s, psi):
""" Creates a model for N two-level systems.
Parameters:
N (int): The number of spins
c (double): The bias for up spins, must be between 0 and 1
(default = 0.5)
"""
# Validate inputs
if not isinstance(N, int):
print("N must be an integer.")
return None
# Construct left vector
Qdag_local = np.zeros((1, 2, 2, 1))
Qdag_local[0, :, :, 0] = np.array([[np.sqrt(1 - c)**-1, 0],
[0, np.sqrt(c)**-1]])
Qdag = mp.mpo(2, N, 1, Qdag_local)
left = mp.apply_operator(copy.deepcopy(psi), Qdag, conjugate=True)
# Store the state of the system
self.size = N
self.c = c
self.s = s
self.psi = psi
self.left = left
self.state = np.zeros(N, dtype=np.bool_)
self.transition_rates = np.zeros(N)
self.original_transition_rates = np.zeros(N)
# Tensor blocks
self.left_blocks = [[] for i in range(N)]
self.right_blocks = [[] for i in range(N)]
return None
def DW_correlation_disconnected(MPS, distance=1):
# Get the number of sites
sites = MPS.length
norm = mp.dot(MPS, MPS)
# Operators
I = np.array([[1, 0], [0, 1]])
n = np.array([[0, 0], [0, 1]])
# Find the amount of pairs
pairs = sites + 1 - distance
# Store correlation
correlation = 0
# Get occupations
occupations = DW_occupation(MPS)
# Loop through each pair
for site in range(pairs):
if distance == 1:
if site == 0:
# Create an MPO to measure
local = np.zeros((1, 2, 2, 1))
local[0, :, :, 0] = I
mpo = mp.mpo(2, sites, 1, local)
site1 = np.zeros((1, 2, 2, 1))
site1[0, :, :, 0] = n
site2 = np.zeros((1, 2, 2, 1))
site2[0, :, :, 0] = I - n
mpo.edit_structure(site, site1)
mpo.edit_structure(site + 1, site2)
elif site == sites - distance:
# Create an MPO to measure
local = np.zeros((1, 2, 2, 1))
local[0, :, :, 0] = I
mpo = mp.mpo(2, sites, 1, local)
site1 = np.zeros((1, 2, 2, 1))
site1[0, :, :, 0] = I - n
site2 = np.zeros((1, 2, 2, 1))
site2[0, :, :, 0] = n
mpo.edit_structure(site - 1, site1)
mpo.edit_structure(site, site2)
else:
# Create an MPO to measure
local = np.zeros((2, 2, 2, 2))
local[0, :, :, 0] = I
local[1, :, :, 1] = I
mpo = mp.mpo(2, sites, 2, local)
if site == 1:
site1 = np.zeros((1, 2, 2, 2))
site1[0, :, :, 0] = n
site1[0, :, :, 1] = I - n
else:
site1 = np.zeros((2, 2, 2, 2))
site1[0, :, :, 0] = n
site1[1, :, :, 1] = I - n
site2 = np.zeros((2, 2, 2, 2))
site2[0, :, :, 0] = I - n
site2[1, :, :, 1] = n
if site == sites - 1 - distance:
site3 = np.zeros((2, 2, 2, 1))
site3[0, :, :, 0] = n
site3[1, :, :, 0] = I - n
else:
site3 = np.zeros((2, 2, 2, 2))
site3[0, :, :, 0] = n
site3[1, :, :, 1] = I - n
if site != 1:
local = np.zeros((1, 2, 2, 2))
local[0, :, :, 0] = I
local[0, :, :, 1] = I
mpo.edit_structure(0, local)
if site != sites - 1 - distance:
local = np.zeros((2, 2, 2, 1))
local[0, :, :, 0] = I
local[1, :, :, 0] = I
mpo.edit_structure(sites - 1, local)
mpo.edit_structure(site - 1, site1)
mpo.edit_structure(site, site2)
mpo.edit_structure(site + 1, site3)
else:
if site == 0:
# Create an MPO to measure
local = np.zeros((2, 2, 2, 2))
local[0, :, :, 0] = I
local[1, :, :, 1] = I
mpo = mp.mpo(2, sites, 2, local)
site1 = np.zeros((1, 2, 2, 2))
site1[0, :, :, 0] = n
site1[0, :, :, 1] = n
site2 = np.zeros((2, 2, 2, 2))
site2[0, :, :, 0] = I - n
site2[1, :, :, 1] = n
site3 = np.zeros((2, 2, 2, 2))
site3[0, :, :, 0] = n
site3[1, :, :, 1] = I - n
site4 = np.zeros((2, 2, 2, 1))
site4[0, :, :, 0] = I
site4[1, :, :, 0] = I
mpo.edit_structure(site, site1)
mpo.edit_structure(site + distance - 1, site2)
mpo.edit_structure(site + distance, site3)
mpo.edit_structure(sites - 1, site4)
elif site == sites - distance:
# Create an MPO to measure
local = np.zeros((2, 2, 2, 2))
local[0, :, :, 0] = I
local[1, :, :, 1] = I
mpo = mp.mpo(2, sites, 2, local)
site1 = np.zeros((2, 2, 2, 2))
site1[0, :, :, 0] = n
site1[1, :, :, 1] = I - n
site2 = np.zeros((2, 2, 2, 2))
site2[0, :, :, 0] = I - n
site2[1, :, :, 1] = n
site3 = np.zeros((2, 2, 2, 1))
site3[0, :, :, 0] = n
site3[1, :, :, 0] = n
site4 = np.zeros((1, 2, 2, 2))
site4[0, :, :, 0] = I
site4[0, :, :, 1] = I
mpo.edit_structure(0, site4)
mpo.edit_structure(site - 1, site1)
mpo.edit_structure(site, site2)
mpo.edit_structure(site - 1 + distance, site3)
else:
# Create an MPO to measure
local = np.zeros((4, 2, 2, 4))
local[0, :, :, 0] = I
local[1, :, :, 1] = I
local[2, :, :, 2] = I
local[3, :, :, 3] = I
mpo = mp.mpo(2, sites, 4, local)
if site == 1:
site1 = np.zeros((1, 2, 2, 4))
site1[0, :, :, 0] = n
site1[0, :, :, 1] = I - n
site1[0, :, :, 2] = n
site1[0, :, :, 3] = I - n
else:
site1 = np.zeros((4, 2, 2, 4))
site1[0, :, :, 0] = n
site1[1, :, :, 1] = I - n
site1[2, :, :, 2] = n
site1[3, :, :, 3] = I - n
site2 = np.zeros((4, 2, 2, 4))
site2[0, :, :, 0] = I - n
site2[1, :, :, 1] = n
site2[2, :, :, 2] = I - n
site2[3, :, :, 3] = n
site3 = np.zeros((4, 2, 2, 4))
site3[0, :, :, 0] = n
site3[1, :, :, 1] = I - n
site3[2, :, :, 2] = I - n
site3[3, :, :, 3] = n
if site == sites - 1 - distance:
site4 = np.zeros((4, 2, 2, 1))
site4[0, :, :, 0] = I - n
site4[1, :, :, 0] = n
site4[2, :, :, 0] = n
site4[3, :, :, 0] = I - n
else:
site4 = np.zeros((4, 2, 2, 4))
site4[0, :, :, 0] = I - n
site4[1, :, :, 1] = n
site4[2, :, :, 2] = n
site4[3, :, :, 3] = I - n
if site != 1:
local = np.zeros((1, 2, 2, 4))
local[0, :, :, 0] = I
local[0, :, :, 1] = I
local[0, :, :, 2] = I
local[0, :, :, 3] = I
mpo.edit_structure(0, local)
if site != sites - 1 - distance:
local = np.zeros((4, 2, 2, 1))
local[0, :, :, 0] = I
local[1, :, :, 0] = I
local[2, :, :, 0] = I
local[3, :, :, 0] = I
mpo.edit_structure(sites - 1, local)
mpo.edit_structure(site - 1, site1)
mpo.edit_structure(site, site2)
mpo.edit_structure(site - 1 + distance, site3)
mpo.edit_structure(site + distance, site4)
correl = mp.expectation(mpo, MPS) / norm
correlation += correl - occupations[site] * occupations[site +
distance]
return correlation / pairs
def DW_occupation(MPS):
# Get the number of sites
sites = MPS.length
# Store occupations
occupations = np.zeros(sites + 1)
norm = mp.dot(MPS, MPS)
# Local operators
I = np.array([[1, 0], [0, 1]])
n = np.array([[0, 0], [0, 1]])
# Loop through each site
for site in range(sites + 1):
if site == 0:
# Create local identity operator
local = np.zeros((1, 2, 2, 1))
local[0, :, :, 0] = I
# Create local n operator
nlocal1 = np.zeros((1, 2, 2, 1))
nlocal1[0, :, :, 0] = n
# Create MPO
ni = mp.mpo(2, sites, 1, local)
ni.edit_structure(site, nlocal1)
# Calculate occupation
occupations[site] = mp.expectation(ni, MPS)
elif site == sites:
# Create local identity operator
local = np.zeros((1, 2, 2, 1))
local[0, :, :, 0] = I
# Create local n operator
nlocal1 = np.zeros((1, 2, 2, 1))
nlocal1[0, :, :, 0] = n
# Create MPO
ni = mp.mpo(2, sites, 1, local)
ni.edit_structure(site - 1, nlocal1)
# Calculate occupation
occupations[site] = mp.expectation(ni, MPS)
else:
# Create local identity operator
local = np.zeros((1, 2, 2, 1))
local[0, :, :, 0] = I
# Create local n operator
nlocal1 = np.zeros((1, 2, 2, 1))
nlocal1[0, :, :, 0] = n
# Create local 1-n operator
nlocal2 = np.zeros((1, 2, 2, 1))
nlocal2[0, :, :, 0] = I - n
# Create MPO
ni1 = mp.mpo(2, sites, 1, local)
ni1.edit_structure(site - 1, nlocal1)
ni1.edit_structure(site, nlocal2)
ni2 = mp.mpo(2, sites, 1, local)
ni2.edit_structure(site - 1, nlocal2)
ni2.edit_structure(site, nlocal1)
# Calculate occupation
occupations[site] += mp.expectation(ni1, MPS)
occupations[site] += mp.expectation(ni2, MPS)
return occupations / norm
def __init__(self,
c,
s,
psi,
num_sites,
tmax,
activity=True,
occupations=True,
AC=False,
AC_low=-2,
AC_points=1000,
timescale=False,
AC_int=False,
AC_int_timescale=False,
correlations=True,
correlations_range=10):
# Set parameters
self.c = c
self.num_sites = psi.length
self.s = s
# Probability distribtion
self.psi = psi
# Left vectors
Qdag_local = np.zeros((1, 2, 2, 1))
Qdag_local[0, :, :, 0] = np.array([[np.sqrt(1 - c)**-1, 0],
[0, np.sqrt(c)**-1]])
Qdag = mp.mpo(2, self.num_sites, 1, Qdag_local)
self.left = mp.apply_operator(copy.deepcopy(self.psi),
Qdag,
conjugate=True)
# Store the number of sites time for each trajectory
self.num_sites = num_sites
self.tmax = tmax
# Create relevent storage
self.num_sims = 0
# Count the activity
self.count_activity = activity
self.activity = 0
# Count the occupations
self.count_occupations = occupations
self.occupations = 0
# Count the correlations
self.count_correlations = correlations
self.correlations = np.zeros(correlations_range)
self.correlations_range = correlations_range
# Count the AC
self.count_AC = AC
self.AC_times = np.zeros(AC_points)
self.AC_times[1:] = np.logspace(AC_low, np.log10(tmax), AC_points - 1)
self.AC = np.zeros(AC_points)
# Count the TI AC
self.count_timescale = timescale
self.timescale = 0
# Count the AC int
self.count_AC_int = AC_int
self.AC_int = np.zeros(AC_points)
# Count the TI AC
self.count_AC_int_timescale = AC_int_timescale
self.AC_int_timescale = 0
self.configs = []
self.escaperates = []
self.original_escaperates = []