String order parameter zeroes and entanglement spectrum crossings do not generally coincide with or indicate the critical times of dynamical quantum phase transitions in quenched 1D topological models.
A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter
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abstract
We provide strong numerical evidence for a dynamical bulk-boundary correspondence in two-dimensional topological matter which manifests itself as boundary contributions to the dynamical free energy and is governed by a two-dimensional non-Hermitian dynamical Loschmidt matrix -- a setting largely unexplored beyond one dimension. Following a quantum quench, in-gap bands emerge in the spectrum of the Loschmidt matrix between successive dynamical quantum phase transitions when the time-evolving Hamiltonian is topological, while they are absent for quenches into the trivial phase in all cases we have studied. By fitting these in-gap bands, we show that they account for the observed boundary contributions to the dynamical free energy thus supporting a direct connection between the spectrum of a non-Hermitian dynamical matrix and topological boundary contributions. Taken together with earlier studies of the one-dimensional case, our results provide a framework to understand and classify dynamical topological phenomena based on the spectral properties of certain non-Hermitian matrices.
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On the Relation Between String Order Parameters, Entanglement, and Dynamical Quantum Phase Transitions in Topological Dynamics
String order parameter zeroes and entanglement spectrum crossings do not generally coincide with or indicate the critical times of dynamical quantum phase transitions in quenched 1D topological models.