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arXiv:2511.19793 · Physical Review Letters

Generalized Landau Paradigm for quantum phases and phase transitions

Xie Chen

hep-thcond-mat.str-elquant-phSubmitted Nov 24, 2025• Announced Nov 26, 2025• 4 citations
arXivHTMLPDF

Abstract

The Landau paradigm is a central dogma for understanding phase and phase transitions in condensed matter systems, yet for decades it has been known that a variety of quantum phases exist beyond the framework. Is there a more general framework that provides a systematic understanding of phase and phase transitions in quantum many-body systems? Recent developments of the notion of generalized symmetry and generalized gauging seem to point to a way to generalize the Landau Paradigm. In this essay, we discuss how `beyond Landau' phases and phase transitions can be captured by a generalized Landau paradigm in terms of the breaking of generalized symmetries, often induced by the generalized gauging procedure facilitated through the topological holography formalism. We also discuss what needs to be understood to make the generalized Landau paradigm useful in the study of quantum phase and phase transitions.

Journal reference
Phys. Rev. Lett. 135, 250001 (2025)
DOI
10.1103/tmvy-vsqd
Comments
6+2 pages, 6 figures

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The Landau paradigm is a central dogma for understanding phase and phase transitions in condensed matter systems, yet for decades it has been known that a variety of quantum phases exist beyond the framework. Is there a more general framework that provides a systematic understanding of phase and phase transitions in quantum many-body systems? Recent developments of the notion of generalized symmetry and generalized gauging seem to point to a way to generalize the Landau Paradigm. In this essay, we discuss how `beyond Landau' phases and phase transitions can be captured by a generalized Landau paradigm in terms of the breaking of generalized symmetries, often induced by the generalized gauging procedure facilitated through the topological holography formalism. We also discuss what needs to be understood to make the generalized Landau paradigm useful in the study of quantum phase and phase transitions.
We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a topological order to organize the space of quantum systems with a global symmetry in one lower dimension. The global symmetry naturally serves as an input for the topological order. In particular, we holographically construct a String Operator Algebra (SOA) which is the building block of symmetric quantum systems with a given symmetry G in one lower dimension. This exposes a vast web of dualities which act on the space of G-symmetric quantum systems. The SOA facilitates the classification of gapped phases as well as their corresponding order parameters and fundamental excitations, while dualities help to navigate and predict various corners of phase diagrams and analytically compute universality classes of phase transitions. A novelty of the approach is that it treats conventional Landau and unconventional topological phase transitions on an equal footing, thereby providing a holographic unification of these seemingly-disparate domains of understanding. We uncover a new feature of gapped phases and their multi-critical points, which we dub fusion structure, that encodes information about which phases and transitions can be dual to each other. Furthermore, we discover that self-dual systems typically posses emergent non-invertible, i.e., beyond group-like symmetries. We apply these ideas to 1+1d 1 + 1 d quantum spin chains with finite Abelian group symmetry, using topologically-ordered systems in 2+1d 2 + 1 d . We predict the phase diagrams of various concrete spin models, and analytically compute the full conformal spectra of non-trivial quantum phase transitions, which we then verify numerically.
Condensed matter is the area of physics which deals with the phases of matter in condensed form with an aim to understand the properties of these phases and the transition between them based on the known laws of physics. This is usually done by figuring out some characteristic properties of the phase which sets it apart from the others, e.g., symmetry, topological order, entanglement, etc. The most common way of characterizing the transition between these phases is the broken symmetry. In this classification method, one finds the symmetry which phase breaks spontaneously during the transition and develops a local long-range order. This is the famous Landau’s symmetry breaking paradigm [ 1 ]. Landau’s symmetry breaking theory is a phenomenological theory which describes the transition from a symmetric phase (high-temperature phases) to a less symmetric/broken symmetry phase (phases at low temperature). A zero-temperature phase transition is also possible (by tuning the parameters of the Hamiltonian) and is known as quantum phase transition [ 2 ]. Although there were other paradigms of phase transition available, like Anderson localization [ 3 ], Berezinsky—Kosterlitz—Thouless transition [ 4 ] (broken symmetry but no long-range order), etc., Landau’s spontaneous symmetry breaking dominated over the others.
A central dogma of twentieth-century condensed matter physics holds that every phase transition either breaks a symmetry spontaneously or restores one—Landau's paradigm. A cluster of recent preprints, drawn primarily from `cond-mat.str-el` and `physics.atom-ph`, collectively challenges this dogma at the level of microscopic mechanism rather than abstract categorical assertion. This synthesis identifies and cross-connects five specific findings: (1) the existence of "twin phases" and "twin condensable algebras" that are inequivalent gapped phases sharing identical anyon content and isomorphic ground-state degeneracy, yet connected by transitions that cannot be cast as any form of symmetry breaking even after gauging [corpus:arxiv:2605.31601v1][corpus:arxiv:2605.31602v1]; (2) the demonstration that spontaneous breaking of non-invertible symmetries can be dual, via generalized gauging, to deconfined quantum critical points of invertible symmetries, establishing a precise duality dictionary rather than a mere analogy [corpus:arxiv:2605.27672v1]; (3) the characterization of order parameters in one-dimensional systems as Lagrangian algebras in the Drinfeld center, providing a tensor-network-computable diagnostic that generalizes the string-order concept beyond the invertible setting [corpus:arxiv:2605.27193v1]; (4) the discovery of "diabolical textures" as a new topological invariant in inhomogeneous systems, producing "unnecessary critical" surfaces stable to interactions [corpus:arxiv:2605.30421v1]; and (5) the identification of an exact factorization line embedded within an antiferromagnetically ordered phase of a Rydberg spin chain, providing an experimentally accessible zero-entanglement reference point for probing these structures [corpus:arxiv:2605.27166v1]. The thesis is that beyond-Landau transitions are not exotic edge cases but arise from a systematic mismatch between the algebraic structure of condensable algebras and the anyon content that naively classifies phases—a mismatch that is detectable, in principle, by tensor-network diagnostics and Rydberg-atom experiments. The primary falsification path is the construction of a gauging sequence that maps any twin-phase transition to a conventional symmetry-breaking transition; no such construction has been exhibited in the corpus. --- 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, 2605.28688v1, 2605.28794v1, 2605.29745v1, 2605.29875v1, 2605.30421v1, 2605.31540v1, 2605.31601v1, 2605.31602v1
This work taps into the idea of gauging finite subgroups of global symmetries in conventional systems to obtain unconventional phases and phase transitions, greatly expanding the conventional Landau paradigm. Assisted by analytical anomaly computations and numerical density-matrix renormalization group calculations, the authors map the ordinary superfluid-insulator transition of the Bose-Hubbard model to novel phase transitions between exotic topological and/or symmetry-breaking phases. The general framework has potential applications in cold atom experiments and digital quantum simulators.