Anomalies of global symmetries on the lattice

• URL: http://arxiv.org/abs/2507.21209v2
• Date: Thu, 07 Aug 2025 16:17:21 GMT
• Title: Anomalies of global symmetries on the lattice
• Authors: Yi-Ting Tu, David M. Long, Dominic V. Else,
• Abstract summary: A lattice anomaly is not a feature of a specific Hamiltonian, but rather is a topological invariant of the symmetry action.<n>We find that lattice anomalies reproduce the expected properties of QFT anomalies in many ways, but also have crucial differences.<n> lattice anomalies have a number of interesting consequences in their own right, including connections to commuting projector models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 't Hooft anomalies of global symmetries play a fundamental role in quantum many-body systems and quantum field theory (QFT). In this paper, we make a systematic analysis of lattice anomalies - the analog of 't Hooft anomalies in lattice systems - for which we give a precise definition. Crucially, a lattice anomaly is not a feature of a specific Hamiltonian, but rather is a topological invariant of the symmetry action. The controlled setting of lattice systems allows for a systematic and rigorous treatment of lattice anomalies, shorn of the technical challenges of QFT. We find that lattice anomalies reproduce the expected properties of QFT anomalies in many ways, but also have crucial differences. In particular, lattice anomalies and QFT anomalies are not, contrary to a common expectation, in one-to-one correspondence, and there can be non-trivial anomalies on the lattice that are infrared (IR) trivial: they admit symmetric trivial gapped ground states, and map to trivial QFT anomalies at low energies. Nevertheless, we show that lattice anomalies (including IR-trivial ones) have a number of interesting consequences in their own right, including connections to commuting projector models, phases of many-body localized (MBL) systems, and quantum cellular automata (QCA). We make substantial progress on the classification of lattice anomalies and develop several theoretical tools to characterize their consequences on symmetric Hamiltonians. Our work places symmetries of quantum many-body lattice systems into a unified theoretical framework and may also suggest new perspectives on symmetries in QFT.

Related papers

• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation [41.94295877935867]
  We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model.<n>We find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation.
  arXiv  Detail & Related papers  (2025-06-23T14:19:35Z)
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry [49.1574468325115]
  We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics.<n>We study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models, and (b) when these symmetries emerge locally around stationary states.
  arXiv  Detail & Related papers  (2024-11-19T02:15:59Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  In the past decade, the concept of symmetry-enriched topological (SET) phases was proposed and their classifications have been systematically studied for bosonic systems.<n>How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Critical spin models from holographic disorder [49.1574468325115]
  We study the behavior of XXZ spin chains with a quasiperiodic disorder not present in continuum holography.<n>Our results suggest the existence of a class of critical phases whose symmetries are derived from models of discrete holography.
  arXiv  Detail & Related papers  (2024-09-25T18:00:02Z)
• Anomaly in open quantum systems and its implications on mixed-state quantum phases [6.356631694532754]
  We develop a systematic approach to characterize the 't Hooft anomaly in open quantum systems. By representing their symmetry transformation through superoperators, we incorporate them in a unified framework. We find that anomalies of bosonic systems are classified by $Hd+2(Ktimes G,U(1))/Hd+2(G,U(1))$ in $d$ spatial dimensions.
  arXiv  Detail & Related papers  (2024-03-21T16:34:37Z)
• Anomalies of Average Symmetries: Entanglement and Open Quantum Systems [0.0]
  We show that anomalous average symmetry implies degeneracy in the density matrix eigenvalues. We discuss several applications in the contexts of many body localization, quantum channels, entanglement phase transitions and also derive new constraints on the Lindbladian evolution of open quantum systems.
  arXiv  Detail & Related papers  (2023-12-14T16:10:49Z)
• Homotopy, Symmetry, and Non-Hermitian Band Topology [4.777212360753631]
  We show that non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. We reveal different Abelian and non-Abelian phases in $mathcalPT$-symmetric systems. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena.
  arXiv  Detail & Related papers  (2023-09-25T18:00:01Z)
• Non-Invertible Defects in Nonlinear Sigma Models and Coupling to Topological Orders [0.0]
  We investigate defects in general nonlinear sigma models in any spacetime dimensions. We use an analogue of the charge-flux attachment to show that the magnetic defects are in general non-invertible. We explore generalizations that couple nonlinear sigma models to topological quantum field theories by defect attachment.
  arXiv  Detail & Related papers  (2022-12-16T17:37:39Z)
• Topological Superfluid Defects with Discrete Point Group Symmetries [0.0]
  We verify exotic magnetic phases of atomic spinor Bose-Einstein condensates that exhibit complex discrete polytope symmetries in their topological defects. We show how filling the vortex line singularities with atoms in a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous symmetries.
  arXiv  Detail & Related papers  (2022-03-15T18:32:23Z)
• Entanglement entropy in the Ising model with topological defects [0.0]
  Entanglement entropy(EE) contains signatures of many universal properties of conformal field theories. We present an ab-initio analysis of EE for the Ising model in the presence of a topological defect.
  arXiv  Detail & Related papers  (2021-11-08T14:26:37Z)
• Tensor network models of AdS/qCFT [69.6561021616688]
  We introduce the notion of a quasiperiodic conformal field theory (qCFT) We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
  arXiv  Detail & Related papers  (2020-04-08T18:00:05Z)

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.