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 »
- Authors:
-
- Univ. of California at San Diego, La Jolla, CA (United States). Dept. of Physics
- Univ. of Kentucky, Lexington, KY (United States). Dept. of Physics and Astronomy
- 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)
- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- 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}
}
Web of Science
Works referenced in this record:
Anyons in an exactly solved model and beyond
journal, January 2006
- Kitaev, Alexei
- Annals of Physics, Vol. 321, Issue 1
Time Dependence of Correlation Functions Following a Quantum Quench
journal, April 2006
- Calabrese, Pasquale; Cardy, John
- Physical Review Letters, Vol. 96, Issue 13
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
Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model
journal, December 2005
- Dziarmaga, Jacek
- Physical Review Letters, Vol. 95, Issue 24
Statistical Mechanics of the Model. I
journal, September 1970
- Barouch, Eytan; McCoy, Barry M.; Dresden, Max
- Physical Review A, Vol. 2, Issue 3
Causality constraints in conformal field theory
journal, May 2016
- Hartman, Thomas; Jain, Sachin; Kundu, Sandipan
- Journal of High Energy Physics, Vol. 2016, Issue 5
Universal Scaling in Fast Quantum Quenches in Conformal Field Theories
journal, April 2014
- Das, Sumit R.; Galante, Damián A.; Myers, Robert C.
- Physical Review Letters, Vol. 112, Issue 17
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
Dynamics of a quantum phase transition and relaxation to a steady state
journal, September 2010
- Dziarmaga, Jacek
- Advances in Physics, Vol. 59, Issue 6
An introduction to lattice gauge theory and spin systems
journal, October 1979
- Kogut, John B.
- Reviews of Modern Physics, Vol. 51, Issue 4
Universality of Abrupt Holographic Quenches
journal, November 2013
- Buchel, Alex; Myers, Robert C.; van Niekerk, Anton
- Physical Review Letters, Vol. 111, Issue 20
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
Quench dynamics across quantum critical points
journal, May 2004
- Sengupta, K.; Powell, Stephen; Sachdev, Subir
- Physical Review A, Vol. 69, Issue 5
Quantum quenches of holographic plasmas
journal, May 2013
- Buchel, Alex; Lehner, Luis; Myers, Robert C.
- Journal of High Energy Physics, Vol. 2013, Issue 5
Quantum quench in interacting field theory: A self-consistent approximation
journal, April 2010
- Sotiriadis, Spyros; Cardy, John
- Physical Review B, Vol. 81, Issue 13
Sudden quenching in the Kitaev honeycomb model: Study of defect and heat generation
journal, November 2012
- Patel, Aavishkar A.; Dutta, Amit
- Physical Review B, Vol. 86, Issue 17
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
Exact results of the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
journal, February 2008
- Chen, Han-Dong; Nussinov, Zohar
- Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 7
Topological Characterization of Quantum Phase Transitions in a Spin- Model
journal, February 2007
- Feng, Xiao-Yong; Zhang, Guang-Ming; Xiang, Tao
- Physical Review Letters, Vol. 98, Issue 8
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
Dynamics of a quantum phase transition in the random Ising model: Logarithmic dependence of the defect density on the transition rate
journal, August 2006
- Dziarmaga, Jacek
- Physical Review B, Vol. 74, Issue 6
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
Exact Results for Quench Dynamics and Defect Production in a Two-Dimensional Model
journal, February 2008
- Sengupta, K.; Sen, Diptiman; Mondal, Shreyoshi
- Physical Review Letters, Vol. 100, Issue 7
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
Slow quench dynamics of the Kitaev model: Anisotropic critical point and effect of disorder
journal, November 2010
- Hikichi, T.; Suzuki, S.; Sengupta, K.
- Physical Review B, Vol. 82, Issue 17
Cosmological experiments in superfluid helium?
journal, October 1985
- Zurek, W. H.
- Nature, Vol. 317, Issue 6037
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
Divergences in open quantum systems
journal, April 2018
- Agón, Cesar; Lawrence, Albion
- Journal of High Energy Physics, Vol. 2018, Issue 4
Quantum quenches and thermalization in SYK models
journal, July 2019
- Bhattacharya, Ritabrata; Jatkar, Dileep P.; Sorokhaibam, Nilakash
- Journal of High Energy Physics, Vol. 2019, Issue 7
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
Divergences in open quantum systems
journal, April 2018
- Agón, Cesar; Lawrence, Albion
- Journal of High Energy Physics, Vol. 2018, Issue 4
Quantum quenches and thermalization in SYK models
journal, July 2019
- Bhattacharya, Ritabrata; Jatkar, Dileep P.; Sorokhaibam, Nilakash
- Journal of High Energy Physics, Vol. 2019, Issue 7
Low-frequency phase diagram of irradiated graphene and a periodically driven spin- chain
journal, May 2018
- Mukherjee, Bhaskar; Mohan, Priyanka; Sen, Diptiman
- Physical Review B, Vol. 97, Issue 20
Quantum dynamics with stochastic reset
journal, September 2018
- Mukherjee, B.; Sengupta, K.; Majumdar, Satya N.
- Physical Review B, Vol. 98, Issue 10
Complexity as a Novel Probe of Quantum Quenches: Universal Scalings and Purifications
journal, February 2019
- Camargo, Hugo A.; Caputa, Pawel; Das, Diptarka
- Physical Review Letters, Vol. 122, Issue 8