Non-unitary time dynamics of topological modes in open planar quantum systems

TL;DR

This paper explores how topological edge modes in open quantum systems evolve over time under non-unitary dynamics, revealing effects like dephasing and quantum Zeno phenomena that influence their survival and revival probabilities.

Contribution

It introduces a framework for analyzing the real-time dynamics of topological modes in open systems using a Lindblad equation with a time-dependent Hamiltonian, highlighting novel decoherence effects.

Findings

Survival probability decreases with dephasing effects during topological to normal insulator transitions.

Revival or condensation probabilities increase with stronger system-environment coupling during reverse evolution.

The phenomena are relevant to real materials with tunable band gaps and various symmetry classes.

Abstract

Nontrivial topological invariant of bulk electronic wavefunctions in two-dimensional quantum crystals leaves its footprints on the edge, dislocation, and corner modes. Here we investigate non-unitary time dynamics of these topological modes in square lattice-based open quantum systems in which the time-dependent Hamiltonian smoothly interpolates between topologically distinct insulators across band gap closing quantum critical points. The temporal dynamics of these modes is described by a Lindblad equation in which the instantaneous Hamiltonian plays the role of the Lindblad operator, thereby allowing the environment to couple with the system through the energy channels (weak measurement protocol). We show that in the presence of such a real time ramp, the survival probability of these modes decreases (increases) in short (long) time scale where the dephasing (quantum Zeno) effect dominates with the increasing amplitude of the system-to-environment coupling, for both slow and fast ramps from a topological to a normal insulating state. For a reverse course of the time evolution, the revival or condensation probability of nucleating such topological modes, otherwise absent in the initial system, increases for stronger system-to-environment coupling. This phenomenon can be attributed to the strong decoherence of the initial mixed state among all the energy eigenstates of the final Hamiltonian which also includes the topological modes, causing their enhanced condensation probability. Our findings can be germane to real open topological materials with time-tunable band gap, and should be applicable to open topological crystals of arbitrary dimension and belonging to any symmetry class.