Dynamics of almost strong edge modes in spin chains away from integrability

TL;DR

This paper investigates the dynamics and stability of almost strong edge modes, akin to Majorana modes, in non-integrable spin chains, revealing how their long lifetime is influenced by an effective inhomogeneous SSH-like model.

Contribution

It introduces a novel Krylov space approach to analyze edge mode dynamics in non-integrable spin chains, linking the mode's stability to a staggered hopping structure.

Findings

Edge mode lifetime is non-perturbatively long due to staggered hopping.

Effective Krylov Hamiltonian resembles an inhomogeneous SSH model.

Continuum limit relates edge mode to a Dirac Hamiltonian with finite mass.

Abstract

Results are presented for the dynamics of an almost strong edge mode which is the quasi-stable Majorana edge mode occurring in non-integrable spin chains. The dynamics of the edge mode is studied using exact diagonalization, and compared with time-evolution with respect to an effective semi-infinite model in Krylov space obtained from the recursion method. The effective Krylov Hamiltonian is found to resemble a spatially inhomogeneous SSH model where the hopping amplitude increases linearly with distance into the bulk, typical of thermalizing systems, but also has a staggered or dimerized structure superimposed on it. The non-perturbatively long lifetime of the edge mode is shown to be due to this staggered structure which diminishes the effectiveness of the linearly growing hopping amplitude. On taking the continuum limit of the Krylov Hamiltonian, the edge mode is found to be equivalent to the quasi-stable mode of a Dirac Hamiltonian on a half line, with a mass which is non-zero over a finite distance, before terminating into a gapless metallic bulk. The analytic estimates are found to be in good agreement with the numerically obtained lifetimes of the edge mode.