Breaking of clustering and macroscopic coherence under the lens of asymmetry measures

TL;DR

This paper investigates how local perturbations in one-dimensional systems with symmetry breaking lead to macroscopic coherence and correlation changes, using asymmetry measures to quantify quantum effects.

Contribution

It introduces the use of Entanglement Asymmetry and Quantum Fisher Information to characterize macroscopic quantum coherence in symmetry-broken systems after local quenches.

Findings

Local quenches amplify quantum interference effects.

Macroscopic quantum coherence emerges throughout the perturbed region.

A generalized inequality links EA and QFI for mixed states.

Abstract

In one-dimensional systems, spontaneous symmetry breaking (SSB) states are fragile by nature, as the injection of a non-zero energy density above the ground state is expected to restore the symmetry. This instability implies that local perturbations can lead to macroscopic correlation profiles, a breaking of clustering properties and even macroscopic quantum superpositions. In this work, we investigate the effect of interaction on this phenomenology by considering an interacting model with conserved domain wall number, that possesses a ferromagnetic ground state breaking the Z2 symmetry of the Hamiltonian. We first show that a local quench in this system amplifies quantum interferences, producing a macroscopic magnetisation profile that directly reflects the scattering phase of the model. Then, we use two asymmetry measures, namely the Entanglement Asymmetry (EA) and Quantum Fisher Information (QFI), to characterise the quantum coherence associated with the fluctuations of the magnetisation. By focusing on subsystems comparable in size to the light-cone of the perturbation, we confirm the emergence of macroscopic quantum coherence throughout the whole perturbed region. Finally, we discuss the link between EA and QFI and show that the variance/EA inequality for pure state can be generalised to a QFI/EA inequality for mixed states.