Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models

TL;DR

This paper introduces new analytic methods to construct quantum lattice models that exhibit entropic order at high temperature, challenging traditional expectations of disorder, and demonstrates various entropic topological phases.

Contribution

It provides novel constructions of high-temperature entropic orders, including continuous symmetry breaking and topological states, with insights into their symmetry properties.

Findings

Constructed 1+1D models with continuous symmetry breaking at high temperature.

Realized high-temperature entropic $p+ip$ chiral topological states in 2+1D.

Identified strong higher form symmetries and spontaneous symmetry breaking in entropic topological orders.

Abstract

High temperature is usually expected to destroy order: as the Gibbs state approaches the infinite-temperature limit, it becomes an equal-weight ensemble over all states and the system is generically disordered. Recent works showed that entropic order can violate this expectation through coupling to bosons in classical lattice models and quantum field theories, where the ordered states have higher entropy. Here we present new analytic methods for constructing quantum lattice models that exhibit entropic orders. In particular, we construct quantum lattice models with continuous symmetry breaking at high temperature in 1+1 dimensions and clarify how entropic order can evade the Hohenberg-Mermin-Wagner theorems. We also construct high-temperature entropic $p+ip$ chiral topological superconducting states in 2+1 dimensions with temperature-independent anyon correlation functions. In addition, we obtain a broad family of high-temperature entropic non-chiral topological orders. We show that the entropic topological orders have strong higher form symmetries at high temperature unlike the conventional topological orders, and the symmetry is spontaneously broken. These results follow from two general constructions that couple a given lattice model with a low-temperature ordered phase either to ordered bosons or, for local commuting-projector Hamiltonians, to more general bosonic degrees of freedom.