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

Abstract

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.

Authors:
;  [1]
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  1. Brookhaven National Lab. (BNL), Upton, NY (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1235878
Alternate Identifier(s):
OSTI ID: 1223583
Report Number(s):
BNL-111704-2016-JA
Journal ID: ISSN 1098-0121; PRBMDO; R&D Project: PO015; KC0202030
Grant/Contract Number:  
SC00112704; AC02-98CH10886
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 92; Journal Issue: 16; Journal ID: ISSN 1098-0121
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

A. J. A. James, and Konik, R. Quantum quenches in two spatial dimensions using chain array matrix product states. United States: N. p., 2015. Web. doi:10.1103/PhysRevB.92.161111.
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A. J. A. James, & Konik, R. Quantum quenches in two spatial dimensions using chain array matrix product states. United States. https://doi.org/10.1103/PhysRevB.92.161111
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A. J. A. James, and Konik, R. Thu . "Quantum quenches in two spatial dimensions using chain array matrix product states". United States. https://doi.org/10.1103/PhysRevB.92.161111. https://www.osti.gov/servlets/purl/1235878.
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@article{osti_1235878,
title = {Quantum quenches in two spatial dimensions using chain array matrix product states},
author = {A. J. A. James and Konik, R.},
abstractNote = {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.},
doi = {10.1103/PhysRevB.92.161111},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 16,
volume = 92,
place = {United States},
year = {Thu Oct 15 00:00:00 EDT 2015},
month = {Thu Oct 15 00:00:00 EDT 2015}
}
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https://doi.org/10.1103/PhysRevB.92.161111
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    Works referencing / citing this record:

    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

    • Piroli, Lorenzo; Vernier, Eric; Calabrese, Pasquale
    • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 6
    • DOI: 10.1088/1742-5468/ab1c52

    Stochastic approach to non-equilibrium quantum spin systems
    journal, January 2019

    • De Nicola, S.; Doyon, B.; Bhaseen, M. J.
    • Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 5
    • DOI: 10.1088/1751-8121/aaf9be

    Controlling dynamical quantum phase transitions
    journal, May 2018

    Quantum dynamics in transverse-field Ising models from classical networks
    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

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