Topological Entanglement-Spectrum Crossing in Quench Dynamics

TL;DR

This paper reveals stable higher-dimensional topological structures in quench dynamics across all Altland-Zirnbauer classes in 1D, using entanglement spectrum crossings as a detection method, with implications for experimental quantum simulations.

Contribution

It introduces a universal framework linking topological structures to quench dynamics and demonstrates entanglement spectrum crossings as a robust topological indicator in 1D systems.

Findings

Entanglement-spectrum crossings indicate topological phases.

Crossings are stable under symmetry-preserving disorder.

Global degeneracies in the many-body spectrum are topologically rooted.

Abstract

We unveil the stable $(d+1)$-dimensional topological structures underlying the quench dynamics for all the Altland-Zirnbauer classes in $d=1$ dimension, and propose to detect such dynamical topology from the time evolution of entanglement spectra. Focusing on systems in classes BDI and D, we find crossings in single-particle entanglement spectra for quantum quenches between different symmetry-protected topological phases. The entanglement-spectrum crossings are shown to be stable against symmetry-preserving disorder and faithfully reflect both $\mathbb{Z}$ (class BDI) and $\mathbb{Z}_2$ (class D) topological characterizations. As a byproduct, we unravel the topological origin of the global degeneracies emerging temporarily in the many-body entanglement spectrum in the quench dynamics of the transverse-field Ising model. These findings can experimentally be tested in ultracold atoms and trapped ions with the help of cutting-edge tomography for quantum many-body states. Our work paves the way towards a systematic understanding of the role of topology in quench dynamics.