A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation

• URL: http://arxiv.org/abs/2007.10562v3
• Date: Fri, 30 Oct 2020 02:16:55 GMT
• Title: A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation
• Authors: Jiaqi Lou, Ce Shen, Chaoyi Chen, Ling-Yan Hung
• Abstract summary: We study gapped boundaries characterized by "fermionic condensates" in 2+1 d topological order. Each of these condensates can be described by a super commutative Frobenius algebra.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study gapped boundaries characterized by "fermionic condensates" in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We also connect these results with topological defects in super modular invariant CFTs. To render our discussion self-contained, we provide a pedagogical review of relevant mathematical results, so that physicists without prior experience in tensor category should be able to pick them up and apply them readily

Related papers

• Probing Topology of Gaussian Mixed States by the Full Counting Statistics [5.072946612096282]
  Recently, a trend in topological physics is extending topological classification to mixed state. We focus on Gaussian mixed states where the modular Hamiltonians of the density matrix are quadratic free fermion models. The bulk-boundary correspondence is then manifested as stable gapless modes of the modular Hamiltonian and degenerate spectrum of the density matrix.
  arXiv  Detail & Related papers  (2024-02-25T02:55:56Z)
• Topological Interfaces of Luttinger Liquids [0.0]
  Topological interfaces of two-dimensional conformal field theories exhibit striking spectral and entanglement characteristics. We show that a topological interface of two Luttinger liquids can be realized by coupling special one-dimensional superconductors. The proposed lattice model provides an experimentally-realizable alternative to spin and anyon chains for the analysis of several conjectured conformal fixed points.
  arXiv  Detail & Related papers  (2023-12-09T12:41:50Z)
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter [0.0]
  We introduce non-Hermitian hyperbolic matter and elucidate its exceptional properties in depth. We use hyperbolic Bloch theory to investigate band structures of hyperbolic lattices in the presence of non-Hermitian on-site gain and loss. Our results unveil an abundance of exceptional degeneracies in hyperbolic non-Hermitian matter.
  arXiv  Detail & Related papers  (2023-06-28T05:31:24Z)
• Bulk-to-boundary anyon fusion from microscopic models [2.025761610861237]
  We study the fusion events between anyons in the bulk and at the boundary in fixed-point models of 2+1-dimensional non-chiral topological order. A recurring theme in our construction is an isomorphism relating twisted cohomology groups to untwisted ones. The results of this work can directly be applied to study logical operators in two-dimensional topological error correcting codes with boundaries described by a twisted gauge theory of a finite group.
  arXiv  Detail & Related papers  (2023-02-03T16:20:36Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Boundary theories of critical matchgate tensor networks [59.433172590351234]
  Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model.
  arXiv  Detail & Related papers  (2021-10-06T18:00:03Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

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.