Absolute anomalies in (2+1)D symmetry-enriched topological states and
exact (3+1)D constructions
- URL: http://arxiv.org/abs/2003.11553v1
- Date: Wed, 25 Mar 2020 18:00:03 GMT
- Title: Absolute anomalies in (2+1)D symmetry-enriched topological states and
exact (3+1)D constructions
- Authors: Daniel Bulmash and Maissam Barkeshli
- Abstract summary: 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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically
ordered phases of matter can be anomalous, which means that they possess an
obstruction to being realized in purely (2+1)D. In this paper we demonstrate
how to compute the anomaly for symmetry-enriched topological (SET) states of
bosons in complete generality. We demonstrate how, given any unitary modular
tensor category (UMTC) and symmetry fractionalization class for a global
symmetry group $G$, one can define a (3+1)D topologically invariant path
integral in terms of a state sum for a $G$ symmetry-protected topological (SPT)
state. We present an exactly solvable Hamiltonian for the system and
demonstrate explicitly a (2+1)D $G$ symmetric surface termination that hosts
deconfined anyon excitations described by the given UMTC and symmetry
fractionalization class. We present concrete algorithms that can be used to
compute anomaly indicators in general. Our approach applies to general symmetry
groups, including anyon-permuting and anti-unitary symmetries. In addition to
providing a general way to compute the anomaly, our result also shows, by
explicit construction, that every symmetry fractionalization class for any UMTC
can be realized at the surface of a (3+1)D SPT state. As a byproduct, this
construction also provides a way of explicitly seeing how the algebraic data
that defines symmetry fractionalization in general arises in the context of
exactly solvable models. In the case of unitary orientation-preserving
symmetries, our results can also be viewed as providing a method to compute the
$\mathcal{H}^4(G, U(1))$ obstruction that arises in the theory of $G$-crossed
braided tensor categories, for which no general method has been presented to
date.
Related papers
- Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.
We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.
We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
arXiv Detail & Related papers (2025-02-03T15:57:50Z) - Soft symmetries of topological orders [0.0]
(2+1)D topological orders possess emergent symmetries given by a group $textAut(mathcalC)$.
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.
arXiv Detail & Related papers (2025-01-06T19:00:00Z) - 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)
Our invariant is invariant under unitary and similarity transforms.
arXiv Detail & Related papers (2024-12-13T19:44:54Z) - Entanglement asymmetry in CFT with boundary symmetry breaking [0.0]
We study the asymmetry of a subsystem $A$ originating from the symmetry-breaking extending into a semi-infinite bulk boundary.
By employing the twist field formalism, we derive a universal expression for the asymmetry.
Our exact analytical findings are validated through numerical simulations in the critical Ising and 3-state Potts models.
arXiv Detail & Related papers (2024-11-15T14:56:03Z) - 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) - Three perspectives on entropy dynamics in a non-Hermitian two-state system [41.94295877935867]
entropy dynamics as an indicator of physical behavior in an open two-state system with balanced gain and loss is presented.
We distinguish the perspective taken in utilizing the conventional framework of Hermitian-adjoint states from an approach that is based on biorthogonal-adjoint states and a third case based on an isospectral mapping.
arXiv Detail & Related papers (2024-04-04T14:45:28Z) - 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) - 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) - 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) - Classification of Exceptional Nodal Topologies Protected by
$\mathcal{PT}$ Symmetry [0.0]
We classify exceptional nodal degeneracies protected by $mathcalPT$ symmetry in up to three dimensions.
These exceptional nodal topologies include previously overlooked possibilities such as second-order knotted surfaces of arbitrary genus, third-order knots and fourth-order points.
arXiv Detail & Related papers (2021-06-08T18:00:00Z)
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.