Emergent Dynamical Translational Symmetry Breaking as an Order Principle for Localization and Topological Transitions

TL;DR

This paper introduces dynamical translational symmetry (DTS) as a unifying principle to understand localization and topological phase transitions through long-time dynamics, providing a new symmetry-based framework beyond equilibrium theories.

Contribution

It defines a dynamical symmetry concept (DTS) and an order parameter (TLTC) that universally characterizes localization and topological transitions, unifying these phenomena.

Findings

TLTC accurately diagnoses Anderson localization transition

TLTC captures many-body localization transition

TLTC reveals topological phase transitions as emergent symmetry breaking

Abstract

Localization transitions represent a fundamental class of continuous phase transitions, yet they occur without any accompanying symmetry breaking. We resolve this by introducing the concept of dynamical translational symmetry (DTS), which is defined not by the Hamiltonian but by the long-time dynamics of local observables. Its order parameter, the time-averaged local translational contrast (TLTC), quantitatively diagnoses whether evolution restores or breaks translational equivalence. We demonstrate that the TLTC universally captures the Anderson localization transition, the many-body localization transition, and topological phase transitions, revealing that these disparate phenomena are unified by the emergent breaking of DTS. This work establishes a unified dynamical-symmetry framework for phases transitions beyond the equilibrium paradigm.