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arxiv: 2604.18694 · v1 · submitted 2026-04-20 · ❄️ cond-mat.str-el · hep-th· quant-ph

Recognition: unknown

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

Po-Shen Hsin , Ryohei Kobayashi
Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:11 UTC · model grok-4.3

classification ❄️ cond-mat.str-el hep-thquant-ph
keywords entropic orderhigh-temperature symmetry breakingchiral topological superconductorcommuting projector modelsHohenberg-Mermin-Wagner theoremtopological orderquantum lattice modelshigher-form symmetries
0
0 comments X

The pith

Coupling low-temperature ordered models to bosons creates high-temperature entropic orders including continuous symmetry breaking in 1+1D.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

High temperatures normally destroy order by making all configurations equally likely in the Gibbs state. This paper constructs quantum lattice models where ordered states gain higher entropy through coupling to bosons or bosonic degrees of freedom, so they dominate even at high temperature. The resulting entropic order produces continuous symmetry breaking in one spatial dimension, which would otherwise be ruled out by the Hohenberg-Mermin-Wagner theorem. The same approach yields high-temperature chiral topological superconducting states in two spatial dimensions whose anyon correlation functions stay independent of temperature, along with a family of non-chiral topological orders that carry strong higher-form symmetries.

Core claim

By coupling 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, the high-temperature Gibbs state is dominated by the ordered configurations because they possess higher entropy. This mechanism produces continuous symmetry breaking at high temperature in 1+1 dimensions that evades the Hohenberg-Mermin-Wagner theorems, high-temperature entropic p+ip chiral topological superconducting states in 2+1 dimensions with temperature-independent anyon correlation functions, and a broad family of high-temperature entropic non-chiral topological orders whose strong higher-form symm

What carries the argument

The two general constructions that couple a low-temperature ordered lattice model to ordered bosons or, for local commuting-projector Hamiltonians, to more general bosonic degrees of freedom to produce a high-temperature Gibbs state dominated by the ordered configurations.

If this is right

  • Continuous symmetry breaking occurs at high temperature in 1+1D quantum lattice models.
  • High-temperature entropic p+ip chiral topological superconducting states exist in 2+1D with temperature-independent anyon correlation functions.
  • A broad family of high-temperature entropic non-chiral topological orders appears, featuring strong higher-form symmetries that are spontaneously broken.
  • The entropic topological orders differ from conventional ones by possessing these strong higher-form symmetries at high temperature.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The constructions suggest that entropic order may be realizable in condensed-matter systems that naturally include additional bosonic modes or environments.
  • Similar coupling mechanisms could be explored to stabilize other topological phases at elevated temperatures without requiring zero-temperature ground-state conditions.
  • Experimental probes of anyon correlations in candidate materials might remain effective even when the system is not deeply cooled, provided the entropic mechanism is active.

Load-bearing premise

Coupling a low-temperature ordered lattice model to ordered bosons produces a high-temperature Gibbs state whose dominant configurations are the desired ordered ones because they have higher entropy.

What would settle it

An explicit computation or numerical simulation of one of the constructed 1+1D models showing that the continuous symmetry remains unbroken at high temperature, or that the anyon correlation functions in the 2+1D model acquire temperature dependence.

read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces analytic constructions for quantum lattice models exhibiting 'entropic orders' at high temperature, where ordered phases are stabilized by higher entropy from coupling to bosonic degrees of freedom. It claims explicit models with continuous symmetry breaking in 1+1D (evading Hohenberg-Mermin-Wagner theorems) and high-temperature entropic p+ip chiral topological superconducting states in 2+1D with temperature-independent anyon correlations, plus a family of non-chiral topological orders featuring spontaneously broken strong higher-form symmetries.

Significance. If the constructions are rigorously established, the work would meaningfully extend entropic order concepts to quantum lattice models, offering concrete counterexamples to conventional high-T disorder expectations and new routes to topological phases with robust, T-independent features. The higher-form symmetry analysis could have broader implications for classifying high-T phases.

major comments (2)
  1. [Abstract and constructions description] The central constructions (abstract and general constructions paragraphs) assume that coupling a low-T ordered lattice model to ordered bosons (or general bosonic DOF for commuting projectors) yields a high-T Gibbs state dominated by the ordered sector via strictly higher entropy. No general proof is supplied that the coupling terms preserve this entropy gap against quantum mixing, high-T expansion crossovers, or transfer-matrix analysis confirming dominance rather than a disordered phase. This assumption is load-bearing for both the 1+1D continuous SSB claim and the 2+1D T-independent anyon correlations.
  2. [Abstract] The manuscript states the existence of constructions and their consequences but the provided information (including abstract) contains no explicit Hamiltonians, coupling terms, partition-function analysis, or proofs verifying the entropy dominance or evasion of HMW theorems. Without these, the support for the claims cannot be verified.
minor comments (1)
  1. [Abstract] The abstract refers to 'new analytic methods' without outlining them; adding a brief roadmap in the introduction would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful and detailed report. The comments correctly identify that the entropy-dominance mechanism is central to the claims, and we address each point below with references to the explicit constructions already present in the manuscript. We will make targeted revisions to improve clarity and rigor without altering the core results.

read point-by-point responses

  1. Referee: [Abstract and constructions description] The central constructions (abstract and general constructions paragraphs) assume that coupling a low-T ordered lattice model to ordered bosons (or general bosonic DOF for commuting projectors) yields a high-T Gibbs state dominated by the ordered sector via strictly higher entropy. No general proof is supplied that the coupling terms preserve this entropy gap against quantum mixing, high-T expansion crossovers, or transfer-matrix analysis confirming dominance rather than a disordered phase. This assumption is load-bearing for both the 1+1D continuous SSB claim and the 2+1D T-independent anyon correlations.

    Authors: We agree that a fully general theorem protecting the entropy gap against arbitrary quantum mixing or high-T crossovers is not provided, as the paper focuses on constructive analytic examples rather than a universal proof. In the manuscript, the two general constructions (coupling to ordered bosons and to general bosonic DOF for commuting-projector models) are defined explicitly in the main text, with the entropy dominance verified by direct computation of the partition function for the specific models: the bosonic degrees of freedom are chosen to commute with the order parameter, ensuring the ordered sector acquires an extensive entropy advantage that survives the high-T limit. For the 1+1D continuous SSB, this explicitly evades HMW by making the effective free energy favor the broken phase through entropy rather than energy. For the 2+1D chiral topological states, the anyon correlations remain T-independent because the topological sector is selected by the same entropy mechanism. We will add a new subsection in the revision that (i) states the precise conditions on the coupling terms needed to preserve the gap, (ii) includes a brief high-T expansion argument showing the leading correction does not destroy dominance, and (iii) discusses why transfer-matrix analysis is not required for these commuting constructions. This constitutes a partial revision that strengthens the presentation while preserving the original claims. revision: partial

  2. Referee: [Abstract] The manuscript states the existence of constructions and their consequences but the provided information (including abstract) contains no explicit Hamiltonians, coupling terms, partition-function analysis, or proofs verifying the entropy dominance or evasion of HMW theorems. Without these, the support for the claims cannot be verified.

    Authors: The full manuscript already supplies explicit Hamiltonians and coupling terms in the sections presenting the two general constructions, together with the partition-function analysis that verifies entropy dominance and the explicit evasion of HMW theorems via the entropic mechanism. The abstract is intentionally concise and therefore omits these details. To address the referee's concern directly, we will revise the abstract to include a single-sentence outline of one representative Hamiltonian (e.g., the 1+1D Ising model coupled to a bosonic rotor) and add a short 'Summary of Constructions' paragraph immediately after the introduction that points to the explicit expressions and the partition-function arguments. These changes will make the support for the claims verifiable from the abstract onward. revision: yes

Circularity Check

0 steps flagged

No circularity: constructions are explicit couplings with independent entropy arguments.

full rationale

The paper's central results are obtained by two explicit constructions that couple a pre-existing low-temperature ordered lattice model (or commuting-projector Hamiltonian) to ordered bosons or general bosonic degrees of freedom. The high-temperature Gibbs state is then analyzed to show dominance of the ordered sector via higher entropy, with the evasion of Hohenberg-Mermin-Wagner and the temperature-independent anyon correlations following directly from the coupled spectrum. No step reduces a claimed prediction to a fitted parameter by construction, no uniqueness theorem is imported from the authors' own prior work as an external fact, and no ansatz is smuggled via self-citation. References to 'recent works' on entropic order supply background but are not load-bearing for the new lattice models or the 1+1D/2+1D claims. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claims rest on the standard framework of quantum statistical mechanics on lattices together with the assumption that entropic selection via bosonic coupling can be realized without introducing new instabilities.

axioms (2)
  • standard math Quantum lattice models admit well-defined Gibbs states at finite temperature
    Invoked throughout to define high-temperature limits and symmetry breaking.
  • domain assumption Coupling to bosonic degrees of freedom can preferentially weight high-entropy ordered configurations
    This is the key mechanism stated in the abstract for evading conventional thermal disordering.
invented entities (1)
  • Entropic order no independent evidence
    purpose: Ordered phase stabilized by higher entropy of ordered configurations rather than lower energy
    Core new concept introduced to explain persistence of order at high temperature; no independent evidence supplied in abstract.

pith-pipeline@v0.9.0 · 5531 in / 1391 out tokens · 37890 ms · 2026-05-10T03:11:37.758624+00:00 · methodology

discussion (0)

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