Soft symmetries of topological orders

• URL: http://arxiv.org/abs/2501.03314v3
• Date: Sun, 27 Apr 2025 13:33:01 GMT
• Title: Soft symmetries of topological orders
• Authors: Ryohei Kobayashi, Maissam Barkeshli,
• Abstract summary: (2+1)D topological orders possess emergent symmetries given by a group $textAut(mathcalC)$.<n>In this paper we discuss cases where $textAut(mathcalC)$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: (2+1)D topological orders possess emergent symmetries given by a group $\text{Aut}(\mathcal{C})$, which consists of the braided tensor autoequivalences of the modular tensor category $\mathcal{C}$ that describes the anyons. In this paper we discuss cases where $\text{Aut}(\mathcal{C})$ has elements that neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged SPT states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, non-invertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. We also demonstrate analogous phenomena in higher dimensions, such as (3+1)D gauge theory with gauge group given by the quaternion group $Q_8$.

Related papers

• Classification of locality preserving symmetries on spin chains [0.0]
  We consider the action of a finite group $G$ by locality preserving automorphisms (quantum cellular automata) on quantum spin chains. We prove that the anomaly of such symmetries provides an isomorphism between the group of stable equivalence classes of symmetries with the cohomology group $H3(G,U(1))$.
  arXiv  Detail & Related papers  (2025-03-19T10:38:57Z)
• A non-semisimple non-invertible symmetry [0.5932505549359508]
  We investigate the action of a non-semisimple, non-invertible symmetry on spin chains.<n>We find a model where a product state and the so-called W state spontaneously break the symmetry.
  arXiv  Detail & Related papers  (2024-12-27T13:27:24Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbour (between unit cells)<n>Our invariant is invariant under unitary and similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Non-invertible SPT, gauging and symmetry fractionalization [2.541410020898643]
  We construct the lattice models for the phases of all the symmetries in the Rep($Q_8$) duality web. We show that these interplay can be explained using the symmetry fractionalization in the 2+1d bulk SET.
  arXiv  Detail & Related papers  (2024-05-24T21:35:55Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles [55.41644538483948]
  We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the transformations symmetry and the corresponding generators. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties.
  arXiv  Detail & Related papers  (2023-01-13T16:25:25Z)
• Higher-group symmetry in finite gauge theory and stabilizer codes [3.8769921482808116]
  A large class of gapped phases of matter can be described by topological finite group gauge theories. We derive the $d$-group global symmetry and its 't Hooft anomaly for topological finite group gauge theories in $(d+1) space-time dimensions. We discuss several applications, including the classification of fermionic SPT phases in (3+1)D for general fermionic symmetry groups.
  arXiv  Detail & Related papers  (2022-11-21T19:00:00Z)
• Classification of (2+1)D invertible fermionic topological phases with symmetry [2.74065703122014]
  We classify invertible fermionic topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups $G_f$. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu.
  arXiv  Detail & Related papers  (2021-09-22T21:02:07Z)
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry [77.34726150561087]
  We present a general construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories. We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.
  arXiv  Detail & Related papers  (2020-04-15T12:21:28Z)
• Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions [0.0]
  We show how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. We present an exactly solvable Hamiltonian for the system and demonstrate explicitly a (2+1)D $G$ symmetric surface termination. Our results can also be viewed as providing a method to compute the $mathcalH4(G, U(1))$ obstruction that arises in the theory of $G$-crossed braided tensor categories.
  arXiv  Detail & Related papers  (2020-03-25T18:00:03Z)
• 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.