(SPT-)LSM theorems from projective non-invertible symmetries

• URL: http://arxiv.org/abs/2409.18113v2
• Date: Tue, 8 Oct 2024 22:27:43 GMT
• Title: (SPT-)LSM theorems from projective non-invertible symmetries
• Authors: Salvatore D. Pace, Ho Tat Lam, Ömer M. Aksoy,
• Abstract summary: Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations. The projectivity also affects the dual symmetries after gauging $mathsfRep(G)times Z(G)$ sub-symmetries.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible symmetries and lattice translations in a generalized $1+1$D quantum XY model based on group-valued qudits. This model is specified by a finite group $G$ and enjoys a projective $\mathsf{Rep}(G)\times Z(G)$ and translation symmetry, where symmetry operators obey a projective algebra in the presence of symmetry defects. For invertible symmetries, such projective algebras imply Lieb-Schultz-Mattis (LSM) anomalies. However, this is not generally true for non-invertible symmetries, and we derive a condition on $G$ for the existence of an LSM anomaly. When this condition is not met, we prove an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak symmetry protected topological (SPT) state with non-trivial entanglement, for which we construct an example fixed-point Hamiltonian. The projectivity also affects the dual symmetries after gauging $\mathsf{Rep}(G)\times Z(G)$ sub-symmetries, giving rise to non-Abelian and non-invertible dipole symmetries, as well as non-invertible translations. We complement our analysis with the SymTFT, where the projectivity causes it to be a topological order non-trivially enriched by translations. Throughout the paper, we develop techniques for gauging $\mathsf{Rep}(G)$ symmetry and inserting its symmetry defects on the lattice, which are applicable to other non-invertible symmetries.

Related papers

• Variational Inference Failures Under Model Symmetries: Permutation Invariant Posteriors for Bayesian Neural Networks [43.88179780450706]
  We investigate the impact of weight space permutation symmetries on variational inference. We devise a symmetric symmetrization mechanism for constructing permutation invariant variational posteriors. We show that the symmetrized distribution has a strictly better fit to the true posterior, and that it can be trained using the original ELBO objective.
  arXiv  Detail & Related papers  (2024-08-10T09:06:34Z)
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections [0.0]
  Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way. In this paper, we systematically study the gauging of finite Abelian modulated symmetries in $1+1$ dimensions.
  arXiv  Detail & Related papers  (2024-06-18T18:00:00Z)
• 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)
• 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)
• 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)
• Remarks on effects of projective phase on eigenstate thermalization hypothesis [0.0]
  We consider $mathbbZ_NtimesmathbbZ_N$ symmetries with nontrivial projective phases. We also perform numerical analyses for $ (1+1)$-dimensional spin chains and the $ (2+1)$-dimensional lattice gauge theory.
  arXiv  Detail & Related papers  (2023-10-17T17:36:37Z)
• Theory of Quantum Circuits with Abelian Symmetries [0.0]
  It was found that generic unitaries respecting a global symmetry cannot be realized, even approximately, using gates that respect the same symmetry. This observation raises important open questions: What unitary transformations can be realized with k-local gates that respect a global symmetry? In this work, we address these questions for the case of Abelian (commutative) symmetries and develop constructive methods for circuits with such symmetries.
  arXiv  Detail & Related papers  (2023-02-24T05:47:13Z)
• 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)
• Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry [85.36456486475119]
  A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
  arXiv  Detail & Related papers  (2021-11-24T15:50:22Z)
• $\PT$ Symmetry and Renormalisation in Quantum Field Theory [62.997667081978825]
  Quantum systems governed by non-Hermitian Hamiltonians with $PT$ symmetry are special in having real energy eigenvalues bounded below and unitary time evolution. We show how $PT$ symmetry may allow interpretations that evade ghosts and instabilities present in an interpretation of the theory within a Hermitian framework.
  arXiv  Detail & Related papers  (2021-03-27T09:46:36Z)
• 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)

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.