Entanglement-enabled symmetry-breaking orders

TL;DR

This paper introduces a new class of symmetry-breaking orders that cannot be represented by tensor-product states, characterized by entanglement properties, with exactly solvable models and potential realizations involving continuous symmetries.

Contribution

It proposes a criterion to identify entanglement-enabled symmetry-breaking orders and provides explicit models demonstrating their properties and topological features.

Findings

Identifies a new class of symmetry-breaking orders beyond tensor-product states.

Constructs exactly solvable 1D models with entanglement-enabled symmetry-breaking.

Shows these states can host protected gapless edge modes and relate to symmetry-protected topological states.

Abstract

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.