skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: An exactly solvable quench protocol for integrable spin models

Abstract

Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field Ising model on a one-dimensional chain and the Kitaev model on a two-dimensional honeycomb lattice using a nonlinear quench protocol which allows for exact analytical solutions of the dynamics. Our quench protocol starts with a finite mass gap at early times and crosses a critical point or a critical region, and we study the behaviour of one point functions of the quenched operator at the critical point or in the critical region as a function of the quench rate. For quench rates slow compared to the initial mass gap, we find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to the mass gap, but slow compared to the inverse lattice spacing, we find scaling behaviour similar to smooth fast continuum quenches. For quench rates of the same order of the lattice scale, the one point function saturates as a function of the rate, approaching the results of an abrupt quench. The presence of an extended critical surface in the Kitaev model leadsmore » to a variety of scaling exponents depending on the starting point and on the time where the operator is measured. We discuss the role of the amplitude of the quench in determining the extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the saturation.« less

Authors:
 [1];  [2]; ORCiD logo [3];  [4];  [5]
  1. Univ. of California at San Diego, La Jolla, CA (United States). Dept. of Physics
  2. Univ. of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
  3. Univ. of Amsterdam, Amsterdam (The Netherlands). Inst. for theoretical Physics Amsterdam and Delta Inst. for Theoretical Physics; Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  4. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  5. Indian Association for the Cultivation of Science, Kolkata (India). Theoretical Physics Dept.
Publication Date:
Research Org.:
Univ. of California, San Diego, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1504773
Grant/Contract Number:  
SC0009919; NSF-PHY-1521045
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Holography and condensed matter physics (AdS/CMT); Integrable Field Theories; Lattice Integrable Models

Citation Formats

Das, Diptarka, Das, Sumit R., Galante, Damián A., Myers, Robert C., and Sengupta, Krishnendu. An exactly solvable quench protocol for integrable spin models. United States: N. p., 2017. Web. doi:10.1007/jhep11(2017)157.
Das, Diptarka, Das, Sumit R., Galante, Damián A., Myers, Robert C., & Sengupta, Krishnendu. An exactly solvable quench protocol for integrable spin models. United States. doi:10.1007/jhep11(2017)157.
Das, Diptarka, Das, Sumit R., Galante, Damián A., Myers, Robert C., and Sengupta, Krishnendu. Fri . "An exactly solvable quench protocol for integrable spin models". United States. doi:10.1007/jhep11(2017)157. https://www.osti.gov/servlets/purl/1504773.
@article{osti_1504773,
title = {An exactly solvable quench protocol for integrable spin models},
author = {Das, Diptarka and Das, Sumit R. and Galante, Damián A. and Myers, Robert C. and Sengupta, Krishnendu},
abstractNote = {Quantum quenches in continuum field theory across critical points are known to display different scaling behaviours in different regimes of the quench rate. We extend these results to integrable lattice models such as the transverse field Ising model on a one-dimensional chain and the Kitaev model on a two-dimensional honeycomb lattice using a nonlinear quench protocol which allows for exact analytical solutions of the dynamics. Our quench protocol starts with a finite mass gap at early times and crosses a critical point or a critical region, and we study the behaviour of one point functions of the quenched operator at the critical point or in the critical region as a function of the quench rate. For quench rates slow compared to the initial mass gap, we find the expected Kibble-Zurek scaling. In contrast, for rates fast compared to the mass gap, but slow compared to the inverse lattice spacing, we find scaling behaviour similar to smooth fast continuum quenches. For quench rates of the same order of the lattice scale, the one point function saturates as a function of the rate, approaching the results of an abrupt quench. The presence of an extended critical surface in the Kitaev model leads to a variety of scaling exponents depending on the starting point and on the time where the operator is measured. We discuss the role of the amplitude of the quench in determining the extent of the slow (Kibble-Zurek) and fast quench regimes, and the onset of the saturation.},
doi = {10.1007/jhep11(2017)157},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 10 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Anyons in an exactly solved model and beyond
journal, January 2006


Time Dependence of Correlation Functions Following a Quantum Quench
journal, April 2006


Universality in fast quantum quenches
journal, February 2015

  • Das, Sumit R.; Galante, Damián A.; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2015, Issue 2
  • DOI: 10.1007/JHEP02(2015)167

Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model
journal, December 2005


Statistical Mechanics of the XY Model. I
journal, September 1970


Causality constraints in conformal field theory
journal, May 2016

  • Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)099

Universal Scaling in Fast Quantum Quenches in Conformal Field Theories
journal, April 2014


Colloquium : Nonequilibrium dynamics of closed interacting quantum systems
journal, August 2011

  • Polkovnikov, Anatoli; Sengupta, Krishnendu; Silva, Alessandro
  • Reviews of Modern Physics, Vol. 83, Issue 3
  • DOI: 10.1103/RevModPhys.83.863

Dynamics of a quantum phase transition and relaxation to a steady state
journal, September 2010


An introduction to lattice gauge theory and spin systems
journal, October 1979


Universality of Abrupt Holographic Quenches
journal, November 2013


Entanglement growth after a global quench in free scalar field theory
journal, November 2016

  • Cotler, Jordan S.; Hertzberg, Mark P.; Mezei, Márk
  • Journal of High Energy Physics, Vol. 2016, Issue 11
  • DOI: 10.1007/JHEP11(2016)166

Quench dynamics across quantum critical points
journal, May 2004


Quantum quenches of holographic plasmas
journal, May 2013

  • Buchel, Alex; Lehner, Luis; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2013, Issue 5
  • DOI: 10.1007/JHEP05(2013)067

Quantum quench in interacting field theory: A self-consistent approximation
journal, April 2010


Sudden quenching in the Kitaev honeycomb model: Study of defect and heat generation
journal, November 2012


Thermalization with chemical potentials, and higher spin black holes
journal, August 2015

  • Mandal, Gautam; Sinha, Ritam; Sorokhaibam, Nilakash
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)013

Exact results of the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
journal, February 2008


Topological Characterization of Quantum Phase Transitions in a Spin- 1 / 2 Model
journal, February 2007


Smooth and fast versus instantaneous quenches in quantum field theory
journal, August 2015

  • Das, Sumit R.; Galante, Damián A.; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2015, Issue 8
  • DOI: 10.1007/JHEP08(2015)073

Quantum quenches in free field theory: universal scaling at any rate
journal, May 2016

  • Das, Sumit R.; Galante, Damián A.; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2016, Issue 5
  • DOI: 10.1007/JHEP05(2016)164

Exact Results for Quench Dynamics and Defect Production in a Two-Dimensional Model
journal, February 2008


Thermal quenches in $ \mathcal{N} $  = 2* plasmas
journal, August 2012

  • Buchel, Alex; Lehner, Luis; Myers, Robert C.
  • Journal of High Energy Physics, Vol. 2012, Issue 8
  • DOI: 10.1007/JHEP08(2012)049

Slow quench dynamics of the Kitaev model: Anisotropic critical point and effect of disorder
journal, November 2010


Cosmological experiments in superfluid helium?
journal, October 1985


    Works referencing / citing this record:

    Entanglement evolution in Lifshitz-type scalar theories
    journal, January 2019

    • Mozaffar, M. Reza Mohammadi; Mollabashi, Ali
    • Journal of High Energy Physics, Vol. 2019, Issue 1
    • DOI: 10.1007/jhep01(2019)137