Destruction of string order after a quantum quench

TL;DR

This paper studies how non-local string order in a spin-1 chain evolves after a quantum quench, showing that it can be abruptly destroyed depending on the symmetry of the post-quench Hamiltonian.

Contribution

It demonstrates the phenomenon of string-order melting and combines numerical matrix product state simulations with analytical short-time expansions to analyze order dynamics.

Findings

String order can be abruptly destroyed after a quench.

Symmetry-breaking in the Hamiltonian leads to loss of string order.

Non-local order parameters behave differently from local ones in quenched dynamics.

Abstract

We investigate the evolution of string order in a spin-1 chain following a quantum quench. After initializing the chain in the Affleck-Kennedy-Lieb-Tasaki state, we analyze in detail how string order evolves as a function of time at different length scales. The Hamiltonian after the quench is chosen either to preserve or to suddenly break the symmetry which ensures the presence of string order. Depending on which of these two situations arises, string order is either preserved or lost even at infinitesimal times in the thermodynamic limit. The fact that non-local order may be abruptly destroyed, what we call string-order melting, makes it qualitatively different from typical order parameters in the manner of Landau. This situation is thoroughly characterized by means of numerical simulations based on matrix product states algorithms and analytical studies based on a short-time expansion for several simplified models.