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arXiv · 1809.06386

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

Matthew F. Lapa·Andrey Gromov·Taylor L. Hughes
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Abstract

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 post-quench dynamics of the system and the quantum fidelity (Loschmidt echo) of the post-quench state. Next, we explain how to define a spin-2 collective variable $\hat{g}_{ab}(t)$ in the matrix models, and we show that for a weak quench (small anisotropy) the dynamics of $\hat{g}_{ab}(t)$ 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 $W_{\infty}$ algebra, and we show that the geometric quench induces nontrivial dynamics for these variables.

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Matthew F. Lapa, Andrey Gromov, Taylor L. Hughes. 2019-01-24. Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory. https://doi.org/10.1103/physrevb.99.075115

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