def _do_ramp(psi_0, H, basis, v, E_final, V_final):
"""
Auxiliary function to evolve the state and calculate the entropies after the
ramp.
--- arguments ---
psi_0: initial state
H: time-dependent Hamiltonian
basis: spin_basis_1d object containing the spin basis (required for Sent)
E_final, V_final: eigensystem of H(t_f) at the end of the ramp t_f=1/(2v)
"""
# determine total ramp time
t_f = 0.5 / v
# time-evolve state from time 0.0 to time t_f
psi = H.evolve(psi_0, 0.0, t_f)
# calculate entanglement entropy
subsys = range(basis.L // 2) # define subsystem
Sent = ent_entropy(psi, basis, chain_subsys=subsys)["Sent"]
# calculate diagonal entropy in the basis of H(t_f)
S_d = diag_ensemble(basis.L, psi, E_final, V_final,
Sd_Renyi=True)["Sd_pure"]
#
return np.asarray([S_d, Sent])
DE_args = {
"density": randint(2),
"alpha": uniform(5),
"rho_d": True,
"Srdm_args": {
"basis": basis
}
}
### pure state
DE = diag_ensemble(L,
psi0,
E2,
V2,
Obs=O_zxz,
delta_t_Obs=False,
delta_q_Obs=False,
Sd_Renyi=False,
Srdm_Renyi=False,
**DE_args)
DE = diag_ensemble(L,
psi0,
E2,
V2,
Obs=O_zxz,
delta_t_Obs=True,
delta_q_Obs=False,
Sd_Renyi=False,
Srdm_Renyi=False,
**DE_args)
DE = diag_ensemble(L,
#
H1=O_pm+O_zxz
H2=O_pm-O_zxz
# diagonalise H
E1,V1 = H1.eigh()
E2,V2 = H2.eigh()
psi0=V1[:,0]
rho0=np.outer(psi0.conj(),psi0)
alpha=uniform(5)
DE_args={"densities":randint(2),"alpha":uniform(5),"rho_d":True,"Srdm_args":{"basis":basis}}
### pure state
DE = diag_ensemble(L,psi0,E2,V2,Obs=O_zxz,delta_t_Obs=False,delta_q_Obs=False,Sd_Renyi=False,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,psi0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=False,Sd_Renyi=False,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,psi0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=True,Sd_Renyi=False,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,psi0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=True,Sd_Renyi=True,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,psi0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=True,Sd_Renyi=True,Srdm_Renyi=True,**DE_args)
### DM
DE = diag_ensemble(L,rho0,E2,V2,Obs=O_zxz,delta_t_Obs=False,delta_q_Obs=False,Sd_Renyi=False,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,rho0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=False,Sd_Renyi=False,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,rho0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=True,Sd_Renyi=False,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,rho0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=True,Sd_Renyi=True,Srdm_Renyi=False,**DE_args)
DE = diag_ensemble(L,rho0,E2,V2,Obs=O_zxz,delta_t_Obs=True,delta_q_Obs=True,Sd_Renyi=True,Srdm_Renyi=True,**DE_args)
### thermal average
beta=[10.0,1.0,0.1]
in_state={'V1':V1,'E1':E1,'f_args':[beta],'V1_state':[0,2,4,6]}
# alternative way by solving Schroedinger's eqn
psi_t = H.evolve(psi_i, t.i, t.vals, rtol=1E-9, atol=1E-9)
meas = obs_vs_time(psi_t, t.vals, {"E_time": HF_02 / L}, Sent_args=Sent_args)
#"""
# read off measurements
Energy_t = meas["E_time"]
Entropy_t = meas["Sent_time"]["Sent"]
#
##### calculate diagonal ensemble measurements
DE_args = {
"Obs": HF_02,
"Sd_Renyi": True,
"Srdm_Renyi": True,
"Srdm_args": Sent_args
}
DE = diag_ensemble(L, psi_i, EF, VF, **DE_args)
Ed = DE["Obs_pure"]
Sd = DE["Sd_pure"]
Srdm = DE["Srdm_pure"]
#
##### plot results #####
import matplotlib.pyplot as plt
import pylab
# define legend labels
str_E_t = "$\\mathcal{E}(lT)$"
str_Sent_t = "$s_\mathrm{ent}(lT)$"
str_Ed = "$\\overline{\mathcal{E}}$"
str_Srdm = "$\\overline{s}_\mathrm{rdm}$"
str_Sd = "$s_d^F$"
# plot infinite-time data
fig = plt.figure()
from quspin.operators import hamiltonian # Hamiltonians and operators from quspin.basis import spin_basis_1d # Hilbert space spin basis from quspin.tools.measurements import diag_ensemble import numpy as np # generic math functions # L=12 # syste size # coupling strenghts J=1.0 # spin-spin coupling h=0.8945 # x-field strength g=0.945 # z-field strength # create site-coupling lists J_zz=[[J,i,(i+1)%L] for i in range(L)] # PBC x_field=[[h,i] for i in range(L)] z_field=[[g,i] for i in range(L)] # create static and dynamic lists static_1=[["x",x_field],["z",z_field]] static_2=[["zz",J_zz],["x",x_field],["z",z_field]] dynamic=[] # create spin-1/2 basis basis=spin_basis_1d(L,kblock=0,pblock=1) # set up Hamiltonian H1=hamiltonian(static_1,dynamic,basis=basis,dtype=np.float64) H2=hamiltonian(static_2,dynamic,basis=basis,dtype=np.float64) # compute eigensystems of H1 and H2 E1,V1=H1.eigh() psi1=V1[:,14] # pick any state as initial state E2,V2=H2.eigh() # # calculate long-time (diagonal ensemble) expectations of H1 and its temporal fluctuations Diag_Ens=diag_ensemble(L,psi1,E2,V2,Obs=H1,delta_t_Obs=True) print(Diag_Ens['Obs_pure'],Diag_Ens['delta_t_Obs_pure'])
