Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory

Lapa, Matthew F.; Gromov, Andrey; Hughes, Taylor L.

doi:10.1103/physrevb.99.075115

Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory

Journal Article · Thu Feb 07 00:00:00 EST 2019 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.99.075115· OSTI ID:1656499

Lapa, Matthew F. ^[1]; Gromov, Andrey ^[2]; Hughes, Taylor L. ^[3]

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

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

{\overset{'}{g}}_{a b} (t)

in the matrix models, and we show that for a weak quench (small anisotropy), the dynamics of

{\overset{'}{g}}_{a b} (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_{\infty}

algebra, and we show that the geometric quench induces nontrivial dynamics for these variables.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1656499

Alternate ID(s):: OSTI ID: 1493853

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 7 Vol. 99; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory

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