A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems

• URL: http://arxiv.org/abs/2605.28925v1
• Date: Wed, 27 May 2026 18:00:00 GMT
• Title: A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems
• Abstract summary: We show how to understand and diagnose strong symmetries and strong-to-weak symmetry breaking in an explicitly local way.<n>We introduce von Neumann systems, which in infinite-volume symmetries are intermediate between strong and weak symmetries.
• Score: 1.0960289997471084
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In mixed states of quantum systems, symmetries come in two types: strong and weak. Furthermore, it has been argued that in quantum many-body systems, strong symmetries can be "spontaneously broken" down to weak symmetries. An issue is that as previously formulated, such "strong-to-weak symmetry breaking" appears to be a fairly non-local effect. In this paper, we show how to understand and diagnose strong symmetries and strong-to-weak symmetry breaking in an explicitly local way. Our main technical tool is a rigorous definition of strong symmetry in the limit of infinite volume, which generalizes the conventional finite-volume definitions, and for which we give several equivalent formulations, including one involving the concept of "local charge coherence". Finally, we introduce von Neumann systems, which in infinite-volume symmetries are intermediate between strong and weak symmetries. We derive a Lieb-Schultz-Mattis type anomaly constraint for von Neumann symmetries (and therefore, in particular, strong symmetries) in quantum spin chains.

Related papers

• Resource-Theoretic Quantifiers of Weak and Strong Symmetry Breaking: Strong Entanglement Asymmetry and Beyond [0.0]
  We provide a framework to track how weak symmetry breaking is irreversibly converted into strong symmetry breaking in open quantum systems.<n>We propose extensions to generalized symmetries and illustrate the qualitative impact of strong symmetry breaking in analytically tractable QFT examples and applications.
  arXiv  Detail & Related papers  (2026-01-28T19:00:00Z)
• Matrix product state classification of 1D multipole symmetry protected topological phases [21.762451041359906]
  We classify one dimensional bosonic symmetry protected topological phases protected respecting multipole symmetries by employing matrix product state formalism.<n>The symmetry action induces projective representations at the ends of an open chain, which we identify via group cohomology.
  arXiv  Detail & Related papers  (2025-09-11T08:26:51Z)
• Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries [20.76275069383104]
  We show that simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras.<n>We show that our work provides a bridge between well-understood topological defect symmetries and those that arise in more realistic models.
  arXiv  Detail & Related papers  (2025-09-03T18:01:22Z)
• Sequential Circuit as Generalized Symmetry on Lattice [19.75535599298441]
  Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc.<n>In this paper, we ask how to obtain the full, potentially non-invertible symmetry action from the unitary sequential circuit.<n>We find that for symmetries that contain the trivial symmetry operator as a fusion outcome, the sequential circuit fully determines the symmetry action and puts various constraints on their fusion.<n>In contrast, for unannihilable symmetries, like that whose corresponding twist is the Cheshire string, a further 1D sequential circuit is needed
  arXiv  Detail & Related papers  (2025-07-30T05:28:27Z)
• Symmetry and Liouville Space Formulation of Decoherence-Free Subsystems [0.0]
  We propose a generic and systematic decoherence-free scheme to encode quantum information into an open quantum system.<n>We primarily concern the permutation symmetry in conjunction with the unitary symmetry.<n>We construct a super-Schur basis, which block-diagonalizes the super-operators that describe the noisy quantum channels.
  arXiv  Detail & Related papers  (2025-07-21T11:17:32Z)
• Kubo-Martin-Schwinger relation for energy eigenstates of SU(2)-symmetric quantum many-body systems [41.94295877935867]
  We show that non-Abelian symmetries may alter conventional thermodynamics.<n>This work helps extend into nonequilibrium physics the effort to identify how non-Abelian symmetries may alter conventional thermodynamics.
  arXiv  Detail & Related papers  (2025-07-09T19:46:47Z)
• SymTFT Approach for Mixed States with Non-Invertible Symmetries [0.0]
  We develop a framework for studying phases of mixed states with strong and weak symmetries.<n>This framework applies not only to group symmetries but also, importantly, to non-invertible symmetries.
  arXiv  Detail & Related papers  (2025-07-07T18:00:02Z)
• Topological response in open quantum systems with weak symmetries [0.0]
  In open quantum systems, the interaction of the system with its environment gives rise to two types of symmetry.<n>We show that weak symmetries can protect topological responses that distinguish different phases of matter.<n>In particular, we show that the coupling to the environment can induce a phase transition to a state protected by weak symmetries.
  arXiv  Detail & Related papers  (2025-04-03T18:00:10Z)
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking [2.9265730100569702]
  We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations.<n>We find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order.<n>We construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
  arXiv  Detail & Related papers  (2024-10-16T18:00:00Z)
• Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators [20.572965801171225]
  Recent developments have extended the discussion of symmetry and its breaking to mixed states. We propose the Wightman correlator as an alternative diagnostic tool.
  arXiv  Detail & Related papers  (2024-10-12T02:04:40Z)
• Spontaneous symmetry breaking in open quantum systems: strong, weak, and strong-to-weak [4.41737598556146]
  We show that strong symmetry always spontaneously breaks into the corresponding weak symmetry. We conjecture that this relation among strong-to-weak symmetry breaking, gapless modes, and symmetry-charge diffusion is general for continuous symmetries.
  arXiv  Detail & Related papers  (2024-06-27T17:55:36Z)
• Efficient quantum algorithms for testing symmetries of open quantum systems [17.55887357254701]
  In quantum mechanics, it is possible to eliminate degrees of freedom by leveraging symmetry to identify the possible physical transitions. Previous works have focused on devising quantum algorithms to ascertain symmetries by means of fidelity-based symmetry measures. We develop alternative symmetry testing quantum algorithms that are efficiently implementable on quantum computers.
  arXiv  Detail & Related papers  (2023-09-05T18:05:26Z)
• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schr\"odinger equation with focusing saturable nonlinearity and PT-symmetric potential [13.844860643212105]
  We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schr"odinger (FNLS) equation. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. We explore the elastic/semi-elastic collision phenomena between symmetric and asymmetric solitons.
  arXiv  Detail & Related papers  (2022-10-01T13:18:22Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.