Macroscopic Quantum States and Universal Correlations in a Disorder-Order Interface Propagating over a 1D Ground State

TL;DR

This paper studies the dynamics of a quantum spin chain interface between disordered and ordered phases, revealing universal subdiffusive scaling, full-range correlations, and macroscopic quantum states in the interfacial region.

Contribution

It introduces a universal scaling framework for the interface dynamics in quantum spin chains and demonstrates the quantum nature of correlations using the transverse-field Ising model.

Findings

Order parameters scale as t^{1/3} over time.

The interfacial region exhibits full-range correlations.

Subsystems in the interface are in macroscopic quantum states.

Abstract

We consider translationally invariant quantum spin-$\frac{1}{2}$ chains with local interactions and a discrete symmetry that is spontaneously broken at zero temperature. We envision experimenters switching off the couplings between two parts of the system and preparing them in independent equilibrium states. One side of the chain is prepared in a disordered phase, and the other in a symmetry-breaking ground state. When the couplings are switched back on, time evolution ensues. We argue that in integrable systems the front separating the ordered region recedes at the maximal velocity of quasiparticle excitations over the ground state. We infer that, generically, the order parameters should vary on a subdiffusive scale of order $t^{1/3}$, where $t$ is time, and their fluctuations should exhibit the same scaling. This interfacial region exhibits full range correlations, indicating that it cannot be decomposed into nearly uncorrelated subsystems. Using the transverse-field Ising chain as a case study, we demonstrate that all order parameters follow the same universal scaling functions. Through an analysis of the skew information, we uncover that the breakdown of cluster decomposition has a quantum contribution: each subsystem within the interfacial region, with extent comparable to the region, exists in a macroscopic quantum state.