The hidden symmetry-breaking picture of symmetry-protected topological order

TL;DR

This paper extends the hidden symmetry-breaking framework to a broad class of one-dimensional SPT phases, linking them to symmetry-broken phases via a non-local unitary transformation, and applies this to systems with continuous symmetries.

Contribution

It generalizes the hidden symmetry-breaking picture of SPT order to more systems, including those with continuous symmetries, using a non-local unitary map.

Findings

Relates SPT phases to symmetry-broken phases through a non-local unitary.

Establishes a connection between string-order and two-point correlation functions.

Applies the framework to systems with SO(2k+1) and SU(k) symmetries.

Abstract

We generalize the hidden symmetry-breaking picture of symmetry-protected topological (SPT) order developed by Kennedy and Tasaki in the context of the Haldane phase. Our generalization applies to a wide class of SPT phases in one-dimensional spin chains, protected by an on-site representation of a finite abelian group. This generalization takes the form of a non-local unitary map that relates local symmetry-respecting Hamiltonians in an SPT phase to local Hamiltonians in a symmetry-broken phase. Using this unitary, we establish a relation between the two-point correlation functions that characterize fully symmetry-broken phases with the string-order correlation functions that characterise the SPT phases, therefore establishing the perspective in these systems that SPT phases are characterised by hidden symmetry-breaking. Our generalization is also applied to systems with continuous symmetries, including SO(2k+1) and SU(k).