Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators

• URL: http://arxiv.org/abs/2401.00505v3
• Date: Thu, 8 Aug 2024 15:09:36 GMT
• Title: Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Authors: Jie-Yu Zhang, Meng-Yuan Li, Peng Ye,
• Abstract summary: We introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter. We show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., line-like subsystems in the 2D cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems.
• Score: 21.052345471463802
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications such as secret sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., line-like subsystems in the 2D cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is \textit{mixed-subsystem SPT} that has either fractal and line-like subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is \textit{chaotic-subsystem SPT} in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in square lattice can be locally simulated by an HOCA generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call \textit{multi-point strange correlators}. We propose a universal procedure to design the spatial configuration of the multi-point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi-point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long range behavior in SRE states.

Related papers

• 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. 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)
• Strong-to-weak spontaneous symmetry breaking meets average symmetry-protected topological order [17.38734393793605]
  We propose a new class of phases, termed the double ASPT phase, which emerges from a nontrivial extension of these two orders. This new phase is absent from prior studies and cannot exist in conventional closed systems.
  arXiv  Detail & Related papers  (2024-10-17T16:36:53Z)
• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems [4.416740212467273]
  We establish a holographic duality between d-dimensional mixed-state symmetry-protected topological phases (mSPTs) and (d+1)-dimensional subsystem symmetry-protected topological states (SSPTs) Specifically, we show that the reduced density matrix of the boundary layer of a (d+1)-dimensional SSPT with subsystem symmetry $mathcalS$ corresponds to a d-dimensional mSPT with strong $mathcalS$ and weak $mathcalG$ symmetries.
  arXiv  Detail & Related papers  (2024-10-10T17:59:42Z)
• Exceptional points in SSH-like models with hopping amplitude gradient [41.94295877935867]
  Recent interest in exceptional points has led to re-examination of non-Hermitian generalizations of many physical models. In such non-Hermitian systems, singular points called exceptional points (EPs) appear that are of interest for applications in super-resolution sensing systems and topological lasers. It is found that while the existence of the EPs is due to the nonreciprocal couplings, the number, position, and order of the EPs can all be altered by the addition of the hopping amplitude gradient.
  arXiv  Detail & Related papers  (2024-08-01T19:09:59Z)
• 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)
• 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)
• Hidden subsystem symmetry protected states in competing topological orders [7.912220713730698]
  We reveal the connection between two-dimensional subsystem symmetry-protected topological (SSPT) states and two-dimensional topological orders via a self-dual frustrated toric code model. This model can be mapped to a model defined on the dual lattice with subsystem symmetries and subextensive ground state degeneracy.
  arXiv  Detail & Related papers  (2023-09-05T15:21:48Z)
• Oracle-Preserving Latent Flows [58.720142291102135]
  We develop a methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles.
  arXiv  Detail & Related papers  (2023-02-02T00:13:32Z)
• 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)
• 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)

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.