Non-Invertible Defects in Nonlinear Sigma Models and Coupling to Topological Orders

• URL: http://arxiv.org/abs/2212.08608v2
• Date: Wed, 28 Dec 2022 09:09:38 GMT
• Title: Non-Invertible Defects in Nonlinear Sigma Models and Coupling to Topological Orders
• Authors: Po-Shen Hsin
• Abstract summary: 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Nonlinear sigma models appear in a wide variety of physics contexts, such as the long-range order with spontaneously broken continuous global symmetries. There are also large classes of quantum criticality admit sigma model descriptions in their phase diagrams without known ultraviolet complete quantum field theory descriptions. We investigate defects in general nonlinear sigma models in any spacetime dimensions, which include the "electric" defects that are characterized by topological interactions on the defects, and the "magnetic" defects that are characterized by the isometries and homotopy groups. We use an analogue of the charge-flux attachment to show that the magnetic defects are in general non-invertible, and the electric and magnetic defects form junctions that combine defects of different dimensions into analogues of higher-group symmetry. We explore generalizations that couple nonlinear sigma models to topological quantum field theories by defect attachment, which modifies the non-invertible fusion and braiding of the defects. We discuss several applications, including constraints on energy scales and scenarios of low energy dynamics with spontaneous symmetry breaking in gauge theories, and axion gauge theories.

Related papers

• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  The interplay between symmetry and topological properties plays a very important role in modern physics. 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. 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)
• Non-invertible duality defects in one, two, and three dimensions via gauging spatially modulated symmetry [15.282090777675679]
  We construct concrete lattice models with non-invertible duality defects via gauging spatially modulated symmetries. Our work provides a unified and systematic analytical framework for constructing exotic duality defects by gauging relevant symmetries.
  arXiv  Detail & Related papers  (2024-09-25T08:52:07Z)
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories [0.0]
  We explore exact generalized symmetries in the standard 2+1d lattice $mathbbZ$ gauge theory coupled to the Ising model. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. We discuss how the symmetries and anomalies in these two models are related by gauging, which is a 2+1d version of the Kennedy-Tasaki transformation.
  arXiv  Detail & Related papers  (2024-05-21T18:00:00Z)
• 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)
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders [37.69303106863453]
  We consider a system of interacting spinless fermions on a two-leg triangular ladder with $pi/2$ magnetic flux per triangular plaquette. Microscopically, the system exhibits a U(1) symmetry corresponding to the conservation of total fermionic charge, and a discrete $mathbbZ$ symmetry. At the intersection of the three phases, the system features a critical point with an emergent SU(2) symmetry.
  arXiv  Detail & Related papers  (2023-05-11T15:57:27Z)
• 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)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• 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)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

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.