# 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}

}

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Works referencing / citing this record:

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Entanglement evolution in Lifshitz-type scalar theories

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