Re: [ALPS-users] Problem with having Sz conserved in TEBD quench - Comp-phys-alps-users

31 Jul 2013


      Hi Joseph,
When you conserve Sz, you should include both
'CONSERVED_QUANTUMNUMBERS' : 'Sz'
and the actual value of the magnetization desired, e.g.
'Sz'    : 0.0
in the parms data.  If you do not put any value for Sz then tebd will work
in the sector with all spins up, as you described.
-Michael
Hello all again,
...
I have been having a problem with my results for quenching a spin-1/2 XXZ
model in the TEBD code and both my colleagues and I are stumped. I am
attempting to study a quench from Delta = 4 to 2 in the XXZ model, starting
from the ground state of the original Hamiltonian, and looking at the local
magnetisation and correlation functions that result. I tried this out in
small systems (around L=32), following the tutorials very closely and
adapting them to my situation, and looking at the local magnetisation. When
I included S_z (the total S_z) as a conserved quantum number in my
parameters, I got no time dependence in my results, with each S_z being 1/2
everywhere along the chain for every time, which seems to be nonsensical.
However, when I removed this constraint, I got (after a much longer
simulation) more sensible results, with a time-dependence and the results
being closer to 0. I am fairly certain that S_z should be conserved here,
so my question is why does this not seem to work? I followed the tutorials
very closely, and those scripts seem to work well enough. The parameter
section of my script is as follows:
import pyalps
import matplotlib.pyplot as plt
import pyalps.plot
import numpy as np
import copy
parms = [ {
    'L'                : 32,
    'MODEL'                : 'spin',
    'local_S'            : 0.5,
    'Jxy'                : 1,
    'Jz'                : 4.0,
    'ITP_CHIS'            : [40, 40, 40],
    'ITP_DTS'            : [0.05, 0.05, 0.025],
    'ITP_CONVS'            : [1E-9, 1E-9, 1E-10],
    'INITIAL_STATE'            : 'ground',
    'CHI_LIMIT'            : 40,
    'TRUNC_LIMIT'            : 1E-12,
    'NUM_THREADS'            : 1,
    'TAUS'                : [0.0, 50.0],
    'POWS'                : [0.0, 1.0],
    'GS'                : ['Jz', 'Jz'],
    'GIS'                : [4.0, 2.0],
    'GFS'                : [2.0, 2.0],
    'NUMSTEPS'            : [100, 2500],
    'STEPSFORSTORE'            : [5, 5]
    } ]
baseName = 'Jz4to2Quench1L32'
nmlname = pyalps.writeTEBDfiles(parms, baseName)
res = pyalps.runTEBD(nmlname)
Data = pyalps.load.loadTimeEvolution(pyalps.getResultFiles(prefix =
'Jz4to2Quench1L32'), measurements = ['Local Magnetization'])
Any help would be greatly appreciated, as my simulations would be much
faster if I could include this!
Thanks,
Joseph Prentice