2025/08/15 by Tomasz Masłowski, Masłowski, Tomasz, Jesko Sirker +3
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Topological Materials and Phenomena
paper · doi:10.48550/arxiv.2508.11521
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.