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