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arXiv:2404.19009 · Physical Review Letters

Classical Origins of Landau-Incompatible Transitions

Abhishodh Prakash, Nick G. Jones

Published Mar 6, 2025• 7 citations
arXivHTMLPDF

Abstract

Continuous phase transitions where symmetry is spontaneously broken are ubiquitous in physics and often found between "Landau-compatible" phases where residual symmetries of one phase are a subset of the other. However, continuous "deconfined quantum critical" transitions between Landau-incompatible symmetry-breaking phases are known to exist in certain quantum systems, often with anomalous microscopic symmetries. In this Letter, we investigate the need for such special conditions. We show that Landau-incompatible transitions can be found in a family of well-known classical statistical mechanical models with anomaly-free symmetries, introduced by José et al. [Phys. Rev. B 16, 1217 (1977).PLRBAQ0556-280510.1103/PhysRevB.16.1217]. The models are anisotropic deformations of the classical 2D XY model labeled by a positive integer Q. For a range of temperatures, even Q models exhibit two Landau-incompatible partial symmetry-breaking phases and a direct transition between them for Q≥4. Characteristic features of deconfined quantum criticality, such as enhanced symmetries and melting of charged defects, are easily seen in a classical setting. For odd Q and corresponding temperature ranges, two regions of a single partial symmetry-breaking phase appear, split by a stable "unnecessary critical" line. We discuss experimental systems that realize these transitions and present anomaly-free quantum models that also exhibit similar phase diagrams.

DOI
10.1103/physrevlett.134.097103

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Continuous phase transitions where symmetry is spontaneously broken are ubiquitous in physics and often found between "Landau-compatible" phases where residual symmetries of one phase are a subset of the other. However, continuous "deconfined quantum critical" transitions between Landau-incompatible symmetry-breaking phases are known to exist in certain quantum systems, often with anomalous microscopic symmetries. In this Letter, we investigate the need for such special conditions. We show that Landau-incompatible transitions can be found in a family of well-known classical statistical mechanical models with anomaly-free symmetries, introduced by José et al. [Phys. Rev. B 16, 1217 (1977).PLRBAQ0556-280510.1103/PhysRevB.16.1217]. The models are anisotropic deformations of the classical 2D XY model labeled by a positive integer Q. For a range of temperatures, even Q models exhibit two Landau-incompatible partial symmetry-breaking phases and a direct transition between them for Q≥4. Characteristic features of deconfined quantum criticality, such as enhanced symmetries and melting of charged defects, are easily seen in a classical setting. For odd Q and corresponding temperature ranges, two regions of a single partial symmetry-breaking phase appear, split by a stable "unnecessary critical" line. We discuss experimental systems that realize these transitions and present anomaly-free quantum models that also exhibit similar phase diagrams.
FINDING: Phase transitions exist that violate the Landau paradigm — they occur without any spontaneous symmetry breaking and are instead governed by topological order and deconfined quantum criticality. | MATH: Landau free energy F = F₀ + a(T−T_c)φ² + bφ⁴ + ... (order parameter φ, symmetry-breaking potential). Beyond-Landau transitions: (1) Deconfined quantum criticality (Senthil et al.) — continuous transition between two ordered phases with *different* broken symmetries, no Ginzburg-Landau order parameter connects them; (2) Topological phase transitions — characterized by topological invariants (Chern number C = (1/2π)∮ F d²k, Z₂ invariant ν, winding numbers), not local order parameters; (3) "Zwillingsphasen" (twin phases) — second-order transition between phases without hidden symmetry breaking. | CONNECTION: Topological invariants are integer-valued (C ∈ ℤ, ν ∈ {0,1}) — quantized, not continuous. This is a *discrete* mathematical structure underlying continuous physical transitions Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
We introduce the concept of twin phases for a symmetry S\mathcal{S}S, defined as inequivalent phases, whose order parameters are part of the same generalized charge under S\mathcal{S}S. Stable, direct transitions between such twin phases are never spontaneous-symmetry-breaking transitions, even after (partially) gauging the initial symmetry S\mathcal{S}S: they are phase transitions without hidden symmetry breaking. We illustrate this with an (anomalous) finite group symmetry in 1+1d, which exhibits such intrinsically beyond Landau transition, i.e. an intrinsically Deconfined Quantum Critical Point (DQCP).
The Landau paradigm—classifying phases by local order parameters and transitions by spontaneous symmetry breaking—has long been understood to be incomplete. Deconfined quantum critical points (DQCPs), topological orders, and symmetry-protected phases resist Landau characterization. A candidate structural pattern now emerging across the cond-mat.str-el corpus is that the failure of the Landau paradigm is not merely an exception but a systematic consequence of three interlocking mechanisms: (1) the presence of non-invertible symmetries whose breaking generates order parameters obeying generalized algebraic structures rather than group representations; (2) the role of anomaly type—specifically the position of the Lieb-Schultz-Mattis (LSM) anomaly class in the Lyndon-Hochschild-Serre spectral sequence—in determining whether a critical point is dual to ordinary symmetry breaking or to non-invertible symmetry breaking; and (3) excitation-density control as the decisive factor separating phases that merely enter the topological regime from those that develop genuine topological order. This synthesis draws on six papers from cond-mat.str-el and one from cond-mat.mes-hall (as a mechanistic comparator), all posted within the last 30 days. The thesis is presented as a *heuristic structural reading*, not a derivation from a shared formalism: the cited papers use distinct mathematical frameworks (fusion categories, spectral sequences, sequential circuits, tensor networks, quadratic fermion mappings), and we argue that these frameworks share a common organizational principle—the algebra of defects and condensable objects—rather than a common Lagrangian. The primary falsification path is explicit: if a direct DQCP transition between twin phases (as defined by [corpus:arxiv:2605.31601v1]) can be shown to be continuously connected to a hidden symmetry-breaking transition upon deformation of the Hamiltonian, the structural independence of beyond-Landau transitions claimed here would be overturned. Numerical DMRG or tensor-network studies on the specific models of [corpus:arxiv:2606.06343v1] and [corpus:arxiv:2605.27672v1] with explicitly broken categorical symmetry would constitute such a test. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.27166v1, 2605.27193v1, 2605.27672v1, 2605.31601v1, 2605.31602v1, 2606.05856v1, 2606.06343v1, 2606.11303v1, 2606.11527v1
Decades of research have revealed a deep understanding of topological quantum matter with protected edge modes. We report that even richer physics emerges when tuning between two topological phases of matter whose respective edge modes are incompatible. The frustration at the edge leads to novel boundary physics, such as symmetry-breaking phases with exotic non-Landau transitions---even when the edge is zero-dimensional. As a minimal case study, we consider spin chains with ${\mathbb{Z}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{3}$ symmetry, exhibiting two nontrivial symmetry-protected topological (SPT) phases. At the bulk 1+1D critical transition between these SPT phases, we find two stable 0+1D boundary phases, each spontaneously breaking one of the Z3{\mathbb{Z}}_{3}Z3​ symmetries. Furthermore, we find that a single boundary parameter tunes a non-Landau boundary critical transition between these two phases. This constitutes a 0+1D version of an exotic phenomenon driven by charged vortex condensation known as deconfined quantum criticality. This work highlights the rich unexplored physics of criticality between nontrivial topological phases and provides insights into the burgeoning field of gapless topological phases.
The Landau-Ginzburg-Wilson theory of phase transitions precludes a continuous transition between two phases that spontaneously break distinct symmetries. However, quantum mechanical effects can intertwine the symmetries, giving rise to an exotic phenomenon called deconfined quantum criticality (DQC). In this Letter, we study the ground state phase diagram of a one-dimensional array of individually trapped neutral atoms interacting strongly via Rydberg states, and demonstrate through extensive numerical simulations that it hosts a variety of symmetry-breaking phases and their transitions including DQC. We show how an enlarged, emergent continuous symmetry arises at the DQCs, which can be experimentally observed in the joint distribution of two distinct order parameters, obtained within measurement snapshots in the standard computational basis. Our findings highlight quantum simulators of Rydberg atoms not only as promising platforms to experimentally realize such exotic phenomena, but also as unique ones allowing access to physical properties not obtainable in traditional experiments.
Deconfined quantum critical points (DQCPs) involving lattice symmetries evade the conventional Landau paradigm because the competing orders break incompatible internal and crystalline symmetries. We show that a class of DQCPs can nevertheless be understood as Landau-type transitions after gauging anomalous onsite symmetries. For spin chains with Lieb-Schultz-Mattis (LSM) anomalies, gauging produces a noninvertible lattice translation whose fusion closes only up to ordinary translations, giving rise to a crystalline categorical symmetry. In the gauged description, the original DQCP becomes a transition between different symmetry breaking patterns of this categorical symmetry. We demonstrate this mechanism in microscopic lattice models; the magnetic-valence-bond-solid (VBS) DQCP realizes a Rep(D8D_8D8​)-type crystalline categorical Landau transition, whereas a y-antiferromagnetic-VBS DQCP realizes a Rep(H8H_8H8​)-type one. Although Rep(D8D_8D8​) and Rep(H8H_8H8​) share the same fusion rules, they have inequivalent FFF-symbols and therefore define distinct categorical descriptions. Our results show that the universal categorical structure underlying these DQCPs is encoded in the full fusion category, rather than in the fusion ring alone.