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  • Open Access

Exploring entropic orders: High-temperature continuous symmetry breaking and topological order

Po-Shen Hsin1,* and Ryohei Kobayashi2,†

  • *Contact author: po-shen.hsin@kcl.ac.uk
  • †Contact author: ryohei.k@ap.t.u-tokyo.ac.jp
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Phys. Rev. B 114, 214112 – Published 29 October, 2026

DOI: https://doi.org/10.1103/ynkx-4f6p

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 nonchiral 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.

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Phys. Rev. B 114, 214112– Published 29 October, 2026
  • Received 29 April 2026
  • Revised 20 July 2026
  • Accepted 13 October 2026
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