Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2204.03045 · Annual Review of Condensed Matter Physics

Generalized Symmetries in Condensed Matter

John McGreevy

Published Oct 20, 2022• 338 citations
arXivHTMLPDF

Abstract

Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This is a brief and elementary review of some of these developments.
DOI
10.1146/annurev-conmatphys-040721-021029

Related papers

Generalized Landau Paradigm for quantum phases and phase transitions

Xie Chen

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.

hep-thCross-listedarXiv:2511.19793•Physical Review Letters•Nov 26, 2025•4 citations

Ordinary Global Symmetries, Phases of Matter, and the Landau Paradigm

Nabil Iqbal

Abstract Chapter 2 of Lectures on Generalized Global Symmetries reviews conventional global symmetries — which are essentially associated with the conservation of densities of particles — from the modern point of view of topological operators. It also briefly discusses the Landau paradigm of the phases of matter, one of the cornerstones of our understanding of nature.

SpringerBriefs in physics•Jan 1, 2025•0 citations

A topological paradigm shift

Jelena Stajic

Topological Matter The discovery of topological phases of matter forced condensed matter physicists to question and reexamine some of the basic notions of their discipline. Wen reviews the progress of the field that took a sharp turn from Landau's broken symmetry paradigm to arrive at the modern notions of topological order and quantum entanglement in many-body systems. This development was made possible by using increasingly sophisticated mathematical formalisms. Science , this issue p. [eaal3099][1] [1]: /lookup/doi/10.1126/science.aal3099

Science•Feb 21, 2019•0 citations

Symmetries and Symmetry Groups in Quantum Physics

Springer eBooks•Apr 16, 2007•0 citations

Symmetry in Many-Body Physics

Vanderlei Salvador Bagnato, R. G. Nazmitdinov, Vyacheslav I. Yukalov

The harmony of nature is expressed through the implementation of symmetry providing optimal structures for complex systems from snowflakes to graphene lattices [...]

Symmetry•Dec 27, 2022•1 citation

Topological Aspects of Strongly Correlated Systems

Gaurav Kumar Gupta

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.

River Publishers eBooks•Sep 30, 2025•0 citations
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.
Topological Matter The discovery of topological phases of matter forced condensed matter physicists to question and reexamine some of the basic notions of their discipline. Wen reviews the progress of the field that took a sharp turn from Landau's broken symmetry paradigm to arrive at the modern notions of topological order and quantum entanglement in many-body systems. This development was made possible by using increasingly sophisticated mathematical formalisms. Science , this issue p. [eaal3099][1] [1]: /lookup/doi/10.1126/science.aal3099
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.