iTEBD

iTEBD simulation for infinite XXZ spin chain

Introduction

The infinite time-evolving block decimation (iTEBD) is an approach to directly search ground state of a system in thermodynamic limit. The infinite XXZ spin chain has been widely studied because of rich quantum phases it appears. It has the Hamiltonian form

H = 0.5 * (SpSn + SnSp) + delta * SzSz

Usage

./itebd_XXZ.py --help

Usage:
    itebd_XXZ.py waveInfo <waveFile> [ --delta DELTA -o OFILE ]
    itebd_XXZ.py contin <waveFile> [ -f PARAMETERFILE -o OFILE --noOutput ]
    itebd_XXZ.py [ -f PARAMETERFILE -o OFILE -w WAVEFILE --noOutput ]
    itebd_XXZ.py -h | --help

Options:
    -h, --help
    -f PARAMETERFILE
    -o OFILE
    -w WAVEFILE
    --delta DELTA   [default: 1.0]

When executing itebd_XXZ.py without any arguments, it tries to read parameter file with filename INPUT as it's input.

Example

INPUT file

DELTA = 1.0
DIMBOUND = 10
TIMESTEP = 0.01o
TIME = 50.0

Start running and its output

./itebd_XXZ.py
# time evolution: ('0.01o', '50.0')
# bound dimension: 10
# delta: 1.0


#    time            energy                    <Sz>                  entropy(A)               entropy(B)     
  +0.000000  +7235.6553863375711444    +355.2224640048209494    -11.1288807672657963     -40.6627246508284941
  +0.010000    -0.2436479669417300      +0.1375887438923357      +1.5929435898235955      +1.4897744849599663
  +0.020000    -0.4168029791991016      +0.1347318164771311      +1.5592893921124045      +1.4448862698034868
  +0.030000    -0.6089846557189831      +0.1046973566161294      +1.5752296688767429      +1.4654981402531972
  +0.040000    -0.7975378306521239      +0.0897392107853261      +1.5764795118318833      +1.4676766913885821
  +0.050000    -0.9906005478819200      +0.0751424247774249      +1.5804350921345940      +1.4754337449769808
  +0.060000    -1.1833449869634665      +0.0621008871724379      +1.5847617934857134      +1.4820810724750597
  +0.070000    -1.3748982673213250      +0.0503676558470213      +1.5895277487103832      +1.4888984990078160
  +0.080000    -1.5633428066555033      +0.0400035137193582      +1.5944496797779175      +1.4952255753142274
  +0.090000    -1.7472583834075524      +0.0309962565597165      +1.5991972050001242      +1.5008896745232396
  +0.100000    -1.9254788352712042      +0.0233079456542218      +1.6035053690217567      +1.5056635976789114
  +0.110000    -2.0971412410904535      +0.0168881410231519      +1.6071123348028622      +1.5093853525661662
  +0.120000    -2.2616550510982196      +0.0116693461037355      +1.6098075674285048      +1.5119378837888919
  +0.130000    -2.4186637832756581      +0.0075769868065606      +1.6114209033060174      +1.5132444903999527
  +0.140000    -2.5680079850891335      +0.0045307767513237      +1.6118254309932658      +1.5132599163700466
  +0.150000    -2.7096863665244189      +0.0024483333781741      +1.6109284136175184      +1.5119587781771486
  +0.160000    -2.8438191882750656      +0.0012465955093000      +1.6086621351863417      +1.5093245046748838
  +0.170000    -2.9706136060783095      +0.0008429955051881      +1.6049735179725981      +1.5053390280069243
  +0.180000    -3.0903327901510904      +0.0011559804878413      +1.5998152682956708      +1.4999749872439201
  +0.190000    -3.2032701039844520      +0.0021052803094770      +1.5931395489010003      +1.4931915418389643
  +0.200000    -3.3097292461457961      +0.0036119538201215      +1.5848950612179575      +1.4849348643054670
  +0.210000    -3.4100101033124313      +0.0055982749758766      +1.5750278609953388      +1.4751437027618164
  +0.220000    -3.5043992103861390      +0.0079874749235400      +1.5634857913796831      +1.4637595435056956
  +0.230000    -3.5931636327827894      +0.0107033984103566      +1.5502259775603391      +1.4507399756534936
  +0.240000    -3.6765476374437478      +0.0136701992939346      +1.5352244394900085      +1.4360732185517127
  +0.250000    -3.7547720505510984      +0.0168122533987641      +1.5184866134677291      +1.4197915941327492
....

Reference

• The iTEBD algorithm beyond unitary evolution