Higher-Order Cellular Automata Generated Symmetry-Protected Topological
Phases and Detection Through Multi-Point Strange Correlators
- URL: http://arxiv.org/abs/2401.00505v2
- Date: Sun, 28 Jan 2024 06:53:01 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: 23.660726551852182
- 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 mixed-subsystem SPT that has either fractal and
line-like subsystem symmetries simultaneously or two distinct types of fractal
symmetries simultaneously. Another example is chaotic 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. 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 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. Our HOCA programs and multi-point
strange correlators pave the way for a unified paradigm to design, classify,
and detect phases of matter with symmetries supported on a great variety of
subsystems, and also provide potential useful perspective in surpassing the
computational irreducibility of HOCA in a quantum mechanical way.
Related papers
- Latent Space Symmetry Discovery [31.28537696897416]
We propose a novel generative model, Latent LieGAN, which can discover symmetries of nonlinear group actions.
We show that our method can express any nonlinear symmetry under some conditions about the group action.
LaLiGAN also results in a well-structured latent space that is useful for downstream tasks including equation discovery and long-term forecasting.
arXiv Detail & Related papers (2023-09-29T19:33:01Z) - 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) - Detecting Subsystem Symmetry Protected Topological Order Through Strange
Correlators [9.02860315442848]
We use strange correlators to detect 2D subsystem symmetry-protected topological phases protected by subsystem symmetries.
We provide the first unbiased large-scale quantum Monte Carlo simulation on the easy and efficient detection in the SSPT phase.
arXiv Detail & Related papers (2022-09-26T18:00:24Z) - 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) - Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and
Fracton Phase Transitions [0.0]
Subsystem symmetry has emerged as a powerful organizing principle for unconventional quantum phases of matter.
We show that certain transitions out of familiar fracton phases, including the X-cube model, can be understood in terms of the spontaneous breaking of subsystem symmetries.
arXiv Detail & Related papers (2021-12-23T17:38:07Z) - 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) - Quantum information dynamics in a high-dimensional parity-time-symmetric
system [3.2363688674314814]
Non-Hermitian systems with parity-time ($mathcalPT$) symmetry give rise to exceptional points (EPs) with exceptional properties.
We simulate quantum dynamics of a four-dimensional $mathcalPT$-symmetric system across a fourth-order exceptional point.
arXiv Detail & Related papers (2021-02-12T19:00:44Z)
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.