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We investigate the recently introduced geometric quench protocol forfractional quantum Hall (FQH) states within the framework of exactly solvablequantum Hall matrix models. In the geometric quench protocol a FQH state issubjected to a sudden change in the ambient geometry, which introducesanisotropy into the system. We formulate this quench in the matrix models andthen we solve exactly for the post-quench dynamics of the system and thequantum fidelity (Loschmidt echo) of the post-quench state. Next, we explainhow to define a spin-2 collective variable $\hat{g}_{ab}(t)$ in the matrixmodels, 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 bythe recently discussed bimetric theory of FQH states. We also find amodification of the bimetric theory such that the predictions of the modifiedbimetric theory agree with those of the matrix model for arbitrarily strongquenches. Finally, we introduce a class of higher-spin collective variables forthe matrix model, which are related to generators of the $W_{\infty}$ algebra,and we show that the geometric quench induces nontrivial dynamics for thesevariables.

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