Title: Quantum quenches in two spatial dimensions using chain array matrix product states

Journal Article · · Physical Review. B, Condensed Matter and Materials Physics
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
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We describe a method for simulating the real time evolution of extended quantum systems in two dimensions (2D). The method combines the benefits of integrability and matrix product states in one dimension to avoid several issues that hinder other applications of tensor based methods in 2D. In particular, it can be extended to infinitely long cylinders. As an example application we present results for quantum quenches in the 2D quantum [(2+1)-dimensional] Ising model. As a result, in quenches that cross a phase boundary we find that the return probability shows nonanalyticities in time.

Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
AC02-98CH10886
OSTI ID:
1235878
Report Number(s):
BNL-111704-2016-JA; KC0202030
Journal Information:
Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 16 Vol. 92; ISSN 1098-0121; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (20)

Dynamical quantum phase transitions (Review Article) journal November 2016
Dynamical quantum phase transitions: a review journal April 2018
Integrable quenches in nested spin chains II: fusion of boundary transfer matrices journal June 2019
Stochastic approach to non-equilibrium quantum spin systems journal January 2019
Sudden expansion and domain-wall melting of strongly interacting bosons in two-dimensional optical lattices and on multileg ladders journal November 2015
Dynamical topological order parameters far from equilibrium journal February 2016
Dynamical quantum phase transitions in the quantum Potts chain journal February 2017
Controlling dynamical quantum phase transitions journal May 2018
Signatures of rare states and thermalization in a theory with confinement journal May 2019
Nonthermal States Arising from Confinement in One and Two Dimensions journal April 2019
Quantum dynamics in transverse-field Ising models from classical networks journal January 2018
Quench dynamics of the Ising field theory in a magnetic field journal January 2018
On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system journal January 2019
Dynamical quantum phase transitions in the quantum Potts chain text January 2017
Dynamical quantum phase transitions: a review text January 2017
Quench dynamics of the Ising field theory in a magnetic field text January 2018
Controlling Dynamical Quantum Phase Transitions text January 2018
Stochastic Approach to Non-Equilibrium Quantum Spin Systems text January 2018
Integrable quenches in nested spin chains II: fusion of boundary transfer matrices text January 2018
On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system text January 2019

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