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 Kitae...
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doaj-4073076c624f4171ad5046a765c8168c2020-11-24T23:20:36ZengSpringerOpenJournal of High Energy Physics1029-84792017-11-0120171114910.1007/JHEP11(2017)157An exactly solvable quench protocol for integrable spin modelsDiptarka Das0Sumit R. Das1Damián A. Galante2Robert C. Myers3Krishnendu Sengupta4Department of Physics, University of California at San DiegoDepartment of Physics and Astronomy, University of KentuckyInstitute for Theoretical Physics Amsterdam and Delta Institute for Theoretical Physics, University of AmsterdamPerimeter Institute for Theoretical PhysicsTheoretical Physics Department, Indian Association for the Cultivation of ScienceAbstract 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.http://link.springer.com/article/10.1007/JHEP11(2017)157Conformal Field TheoryHolography and condensed matter physics (AdS/CMT)Integrable Field TheoriesLattice Integrable Models |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Diptarka Das Sumit R. Das Damián A. Galante Robert C. Myers Krishnendu Sengupta |
spellingShingle |
Diptarka Das Sumit R. Das Damián A. Galante Robert C. Myers Krishnendu Sengupta An exactly solvable quench protocol for integrable spin models Journal of High Energy Physics Conformal Field Theory Holography and condensed matter physics (AdS/CMT) Integrable Field Theories Lattice Integrable Models |
author_facet |
Diptarka Das Sumit R. Das Damián A. Galante Robert C. Myers Krishnendu Sengupta |
author_sort |
Diptarka Das |
title |
An exactly solvable quench protocol for integrable spin models |
title_short |
An exactly solvable quench protocol for integrable spin models |
title_full |
An exactly solvable quench protocol for integrable spin models |
title_fullStr |
An exactly solvable quench protocol for integrable spin models |
title_full_unstemmed |
An exactly solvable quench protocol for integrable spin models |
title_sort |
exactly solvable quench protocol for integrable spin models |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2017-11-01 |
description |
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 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. |
topic |
Conformal Field Theory Holography and condensed matter physics (AdS/CMT) Integrable Field Theories Lattice Integrable Models |
url |
http://link.springer.com/article/10.1007/JHEP11(2017)157 |
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