Enriched string-net models and their excitations

• URL: http://arxiv.org/abs/2305.14068v2
• Date: Tue, 19 Mar 2024 15:36:12 GMT
• Title: Enriched string-net models and their excitations
• Authors: David Green, Peter Huston, Kyle Kawagoe, David Penneys, Anup Poudel, Sean Sanford,
• Abstract summary: Boundaries of Walker-Wang models have been used to construct commuting projector models. This article gives a rigorous treatment of this 2D boundary model. We also use TQFT techniques to show the 3D bulk point excitations of the Walker-Wang bulk are given by the M"uger center.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Boundaries of Walker-Wang models have been used to construct commuting projector models which realize chiral unitary modular tensor categories (UMTCs) as boundary excitations. Given a UMTC $\mathcal{A}$ representing the Witt class of an anomaly, the article [arXiv:2208.14018] gave a commuting projector model associated to an $\mathcal{A}$-enriched unitary fusion category $\mathcal{X}$ on a 2D boundary of the 3D Walker-Wang model associated to $\mathcal{A}$. That article claimed that the boundary excitations were given by the enriched center/M\"uger centralizer $Z^\mathcal{A}(\mathcal{X})$ of $\mathcal{A}$ in $Z(\mathcal{X})$. In this article, we give a rigorous treatment of this 2D boundary model, and we verify this assertion using topological quantum field theory (TQFT) techniques, including skein modules and a certain semisimple algebra whose representation category describes boundary excitations. We also use TQFT techniques to show the 3D bulk point excitations of the Walker-Wang bulk are given by the M\"uger center $Z_2(\mathcal{A})$, and we construct bulk-to-boundary hopping operators $Z_2(\mathcal{A})\to Z^{\mathcal{A}}(\mathcal{X})$ reflecting how the UMTC of boundary excitations $Z^{\mathcal{A}}(\mathcal{X})$ is symmetric-braided enriched in $Z_2(\mathcal{A})$. This article also includes a self-contained comprehensive review of the Levin-Wen string net model from a unitary tensor category viewpoint, as opposed to the skeletal $6j$ symbol viewpoint.

Related papers

• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States [0.0]
  In random tensor networks (RTNs) it was found that the dominant saddles computing the even R'enyi negativity $mathcalE (2k)$ generically break the $mathbbZ_2k$ replica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques. We show that in general holographic states, the saddles computing $mathcalE (2k)$ indeed break the $mathbbZ_2k$ replica symmetry.
  arXiv  Detail & Related papers  (2024-09-19T18:00:00Z)
• Exploring topological entanglement through Dehn surgery [1.3328842853079743]
  We compute the partition function of a closed 3-manifold obtained from Dehn fillings of the link complement. We have given explicit results for all hyperbolic knots $mathcalK$ up to six crossings.
  arXiv  Detail & Related papers  (2024-02-12T07:38:14Z)
• Provably learning a multi-head attention layer [55.2904547651831]
  Multi-head attention layer is one of the key components of the transformer architecture that sets it apart from traditional feed-forward models. In this work, we initiate the study of provably learning a multi-head attention layer from random examples. We prove computational lower bounds showing that in the worst case, exponential dependence on $m$ is unavoidable.
  arXiv  Detail & Related papers  (2024-02-06T15:39:09Z)
• Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
  A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance. The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
  arXiv  Detail & Related papers  (2023-05-22T11:00:25Z)
• Quantized charge polarization as a many-body invariant in (2+1)D crystalline topological states and Hofstadter butterflies [14.084478426185266]
  We show how to define a quantized many-body charge polarization $vecmathscrP$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field. We derive colored Hofstadter butterflies, corresponding to the quantized value of $vecmathscrP$, which further refine the colored butterflies from the Chern number and discrete shift.
  arXiv  Detail & Related papers  (2022-11-16T19:00:00Z)
• Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model [77.34726150561087]
  We provide a systematic treatment of boundaries based on subgroups $Ksubseteq G$ with the Kitaev quantum double $D(G)$ model in the bulk. The boundary sites are representations of a $*$-subalgebra $Xisubseteq D(G)$ and we explicate its structure as a strong $*$-quasi-Hopf algebra. As an application of our treatment, we study patches with boundaries based on $K=G$ horizontally and $K=e$ vertically and show how these could be used in a quantum computer
  arXiv  Detail & Related papers  (2022-08-12T15:05:07Z)
• Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
  The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$. It is assumed that a density matrix $rho$ can be determined from the expectation values of observables. Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
  arXiv  Detail & Related papers  (2021-12-14T16:29:53Z)
• Construction of a new three boson non-hermitian Hamiltonian associated to deformed Higgs algebra: real eigenvalues and Partial PT-symmetry [0.0]
  Fusion of Jordan-Schwinger realization of complexified $mathfraksu(2)$ with Dyson-Maleev representation. Non-hermitian Hamiltonian has real eigenvalues and eigensymmetry inducedity.
  arXiv  Detail & Related papers  (2021-11-07T06:40:47Z)
• Model Selection with Near Optimal Rates for Reinforcement Learning with General Model Classes [27.361399036211694]
  We address the problem of model selection for the finite horizon episodic Reinforcement Learning (RL) problem. In the model selection framework, instead of $mathcalP*$, we are given $M$ nested families of transition kernels. We show that textttARL-GEN obtains a regret of $TildemathcalO(d_mathcalE*H2+sqrtd_mathcalE* mathbbM* H2 T)$
  arXiv  Detail & Related papers  (2021-07-13T05:00:38Z)
• Quantum double aspects of surface code models [77.34726150561087]
  We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry. We show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$.
  arXiv  Detail & Related papers  (2021-06-25T17:03:38Z)
• Model-Based Reinforcement Learning with Value-Targeted Regression [48.92439657407732]
  We focus on finite-horizon episodic RL where the transition model $P$ belongs to a known family of models $mathcalP$. We derive a bound on the regret, which, in the special case of linear mixtures, the regret bound takes the form $tildemathcalO(dsqrtH3T)$.
  arXiv  Detail & Related papers  (2020-06-01T17:47:53Z)

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.