Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory
Abstract
In this work, we investigate the recently introduced geometric quench protocol for fractional quantum Hall (FQH) states within the framework of exactly solvable quantum Hall matrix models. In the geometric quench protocol, a FQH state is subjected to a sudden change in the ambient geometry, which introduces anisotropy into the system. We formulate this quench in the matrix models and then we solve exactly for the postquench dynamics of the system and the quantum fidelity (Loschmidt echo) of the postquench state. Next, we explain how to define a spin-2 collective variable in the matrix models, and we show that for a weak quench (small anisotropy), the dynamics of agrees with the dynamics of the intrinsic metric governed by the recently discussed bimetric theory of FQH states. We also find a modification of the bimetric theory such that the predictions of the modified bimetric theory agree with those of the matrix model for arbitrarily strong quenches. Finally, we introduce a class of higher-spin collective variables for the matrix model, which are related to generators of the algebra, and we show that the geometric quench induces nontrivial dynamics for these variables.
- Authors:
-
- Univ. of Chicago, IL (United States). Kadanoff Center for Theoretical Physics
- Univ. of Chicago, IL (United States). Kadanoff; Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Univ. of Illinois at Urbana-Champaign, IL (United States). Inst. for Condensed Matter Theory
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1656499
- Alternate Identifier(s):
- OSTI ID: 1493853
- Grant/Contract Number:
- AC02-05CH11231; DMR-1351895; DMR-1420709
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Chern-Simons gauge theory; fractional quantum Hall effect; quantum Hall effect
Citation Formats
Lapa, Matthew F., Gromov, Andrey, and Hughes, Taylor L. Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory. United States: N. p., 2019.
Web. doi:10.1103/physrevb.99.075115.
Lapa, Matthew F., Gromov, Andrey, & Hughes, Taylor L. Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory. United States. https://doi.org/10.1103/physrevb.99.075115
Lapa, Matthew F., Gromov, Andrey, and Hughes, Taylor L. Thu .
"Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory". United States. https://doi.org/10.1103/physrevb.99.075115. https://www.osti.gov/servlets/purl/1656499.
@article{osti_1656499,
title = {Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory},
author = {Lapa, Matthew F. and Gromov, Andrey and Hughes, Taylor L.},
abstractNote = {In this work, we investigate the recently introduced geometric quench protocol for fractional quantum Hall (FQH) states within the framework of exactly solvable quantum Hall matrix models. In the geometric quench protocol, a FQH state is subjected to a sudden change in the ambient geometry, which introduces anisotropy into the system. We formulate this quench in the matrix models and then we solve exactly for the postquench dynamics of the system and the quantum fidelity (Loschmidt echo) of the postquench state. Next, we explain how to define a spin-2 collective variable g'ab(t) in the matrix models, and we show that for a weak quench (small anisotropy), the dynamics of g'ab(t) agrees with the dynamics of the intrinsic metric governed by the recently discussed bimetric theory of FQH states. We also find a modification of the bimetric theory such that the predictions of the modified bimetric theory agree with those of the matrix model for arbitrarily strong quenches. Finally, we introduce a class of higher-spin collective variables for the matrix model, which are related to generators of the W∞ algebra, and we show that the geometric quench induces nontrivial dynamics for these variables.},
doi = {10.1103/physrevb.99.075115},
journal = {Physical Review. B},
number = 7,
volume = 99,
place = {United States},
year = {Thu Feb 07 00:00:00 EST 2019},
month = {Thu Feb 07 00:00:00 EST 2019}
}
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