Disentangling modular Walker-Wang models via fermionic invertible boundaries

• URL: http://arxiv.org/abs/2208.03397v2
• Date: Tue, 4 Oct 2022 15:03:41 GMT
• Title: Disentangling modular Walker-Wang models via fermionic invertible boundaries
• Authors: Andreas Bauer
• Abstract summary: Walker-Wang models are fixed-point models of topological order in $3+1$ dimensions constructed from a braided fusion category. We explicitly show triviality of the model by constructing an invertible domain wall to vacuum and a disentangling local unitary circuit. We also discuss general (non-invertible) boundaries of general Walker-Wang models and describe a simple axiomatization of extended TQFT in terms of tensors.
• Score: 1.479413555822768
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Walker-Wang models are fixed-point models of topological order in $3+1$ dimensions constructed from a braided fusion category. For a modular input category $\mathcal M$, the model itself is invertible and is believed to be in a trivial topological phase, whereas its standard boundary is supposed to represent a $2+1$-dimensional chiral phase. In this work we explicitly show triviality of the model by constructing an invertible domain wall to vacuum as well as a disentangling local unitary circuit in the case where $\mathcal M$ is a Drinfeld center. Moreover, we show that if we allow for fermionic (auxiliary) degrees of freedom inside the disentangling domain wall or circuit, the model becomes trivial for a larger class of modular fusion categories, namely those in the Witt classes generated by the Ising UMTC. In the appendices, we also discuss general (non-invertible) boundaries of general Walker-Wang models and describe a simple axiomatization of extended TQFT in terms of tensors.

Related papers

• Entanglement renormalization of fractonic anisotropic $\mathbb{Z}_N$ Laplacian models [4.68169911641046]
  Gapped fracton phases constitute a new class of quantum states of matter which connects to topological orders but does not fit easily into existing paradigms. We investigate the anisotropic $mathbbZ_N$ Laplacian model which can describe a family of fracton phases defined on arbitrary graphs.
  arXiv  Detail & Related papers  (2024-09-26T18:36:23Z)
• Categorical Quantum Volume Operator [41.94295877935867]
  We show a generalization of the quantum volume operator quantifying the volume in curved three-dimensional discrete geometries. In both cases, we obtain a volume operator that is Hermitian, provided that the input category is unitary. As an illustrative example, we consider the case of $mathrmSU(2)_k$ and show that the standard $mathrmSU(2)$ volume operator is recovered in the limit $krightarrowinfty$
  arXiv  Detail & Related papers  (2024-06-04T08:37:10Z)
• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Enriched string-net models and their excitations [0.0]
  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.
  arXiv  Detail & Related papers  (2023-05-23T13:45:33Z)
• Theory of free fermions under random projective measurements [43.04146484262759]
  We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers. We derive a non-linear sigma model (NLSM) as an effective field theory of the problem.
  arXiv  Detail & Related papers  (2023-04-06T15:19:33Z)
• Dualities in one-dimensional quantum lattice models: topological sectors [0.0]
  We construct a general framework for relating the spectra of dual theories to each other. We find that the mapping between its topological sectors and those of the XXZ model is associated with the non-trivial braided auto-equivalence of the Drinfel'd center.
  arXiv  Detail & Related papers  (2022-11-07T18:54:57Z)
• Super-model ecosystem: A domain-adaptation perspective [101.76769818069072]
  This paper attempts to establish the theoretical foundation for the emerging super-model paradigm via domain adaptation. Super-model paradigms help reduce computational and data cost and carbon emission, which is critical to AI industry.
  arXiv  Detail & Related papers  (2022-08-30T09:09:43Z)
• Towards Non-Invertible Anomalies from Generalized Ising Models [4.619541348328937]
  We present a general approach to the bulk-boundary correspondence of noninvertible topological phases, including both topological and fracton orders. This is achieved by a novel bulk construction protocol where solvable $(d+1)$-dimensional bulk models with noninvertible topology are constructed. A single anomalous theory can be realized on the boundaries of two distinct bulk fracton models, a phenomenon not expected in the case of topological orders.
  arXiv  Detail & Related papers  (2022-08-19T00:30:26Z)
• A critical lattice model for a Haagerup conformal field theory [0.0]
  We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions. We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory.
  arXiv  Detail & Related papers  (2021-10-07T14:57:52Z)
• Quantum anomalous Hall phase in synthetic bilayers via twistless twistronics [58.720142291102135]
  We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions. We show that our system exhibits topologicalband structures under appropriate conditions.
  arXiv  Detail & Related papers  (2020-08-06T19:58:05Z)

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.