Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions

• URL: http://arxiv.org/abs/2403.18573v1
• Date: Wed, 27 Mar 2024 13:54:45 GMT
• Title: Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions
• Authors: Jose Garre Rubio, Andras Molnar, Yoshiko Ogata,
• Abstract summary: We consider the classification problem of quantum spin chains invariant under local decomposable group actions. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological phases.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the classification problem of quantum spin chains invariant under local decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated to them. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological (SPT) phases. We prove that these invariants coincide with the ones of [J. Garre Rubio et al, Quantum 7, 927 (2023)] using matrix product states (MPSs) techniques, by explicitly working out the GNS representation of MPSs and MPUs, resulting in a useful dictionary between both approaches that could be of independent interest.

Related papers

• Symmetries from outer automorphisms and unorthodox group extensions [0.0]
  Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs) We discuss how to construct symmetries of QFTs by extending minimal "seed" symmetry groups to larger groups that contain the seed as subgroup(s) We show that all symmetry groups, including the different possible classes of CP and continuous symmetry groups, can be obtained from extensions of the smallest possible symmetry CP1 by consecutive outer automorphisms.
  arXiv  Detail & Related papers  (2024-10-14T19:59:22Z)
• Classification of symmetry protected states of quantum spin chains for continuous symmetry groups [0.0]
  We show that SPT's corresponding to finite on-site symmetry groups $G$ are classified by the second cohomology group $H2(G,U(1))$. We also strengthen the existing results in the sense that our classification results hold within the class of spin chains with locally bounded on-site dimensions.
  arXiv  Detail & Related papers  (2024-09-02T09:41:13Z)
• 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)
• 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)
• 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)
• Classifying phases protected by matrix product operator symmetries using matrix product states [0.0]
  We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry.
  arXiv  Detail & Related papers  (2022-03-23T17:25:30Z)
• One-dimensional symmetric phases protected by frieze symmetries [0.0]
  We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions.
  arXiv  Detail & Related papers  (2022-02-25T18:41:26Z)
• Group Equivariant Conditional Neural Processes [30.134634059773703]
  We present the group equivariant conditional neural process (EquivCNP) We show that EquivCNP achieves comparable performance to conventional conditional neural processes in a 1D regression task.
  arXiv  Detail & Related papers  (2021-02-17T13:50:07Z)
• Constraints on Maximal Entanglement Under Groups of Permutations [73.21730086814223]
  Sets of entanglements are inherently equal, lying in the same orbit under the group action. We introduce new, generalized relationships for the maxima of those entanglement by exploiting the normalizer and normal subgroups of the physical symmetry group.
  arXiv  Detail & Related papers  (2020-11-30T02:21:22Z)
• Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries [0.0]
  We extend the formalism of Matrix Product States to describe one-dimensional gapped systems of fermions with unitary and anti-unitary symmetries. We also consider systems with orientation-reversing spatial symmetries.
  arXiv  Detail & Related papers  (2017-09-30T02:46:22Z)

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.