Fermion condensation and gapped domain walls in topological orders

Wan, Yidun; Wang, Chenjie

doi:10.1007/jhep03(2017)172

Cited by 24 publications

(32 citation statements)

References 50 publications

(173 reference statements)

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“…[76]; see also Refs. [73,74,97] for related earlier applications. The essential role played by proximity-induced superconductivity also becomes clear from this vantage point.…”

Section: Sewing a Non-abelian Spin Liquid To An Electronic Quantumentioning

confidence: 99%

Electrical Probes of the Non-Abelian Spin Liquid in Kitaev Materials

et al. 2020

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Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin-liquid phase in the Kitaev material α-RuCl 3. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid's hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to "perfectly" convert electrons from the former into emergent fermions in the latter-thereby enabling variations of transport probes invented for topological superconductors and fractional quantum-Hall states. Along the way, we resolve puzzles in the literature concerning interacting Majorana fermions, and also develop an anyon-interferometry framework that incorporates nontrivial energy-partitioning effects. Our results illuminate a partial pathway toward topological quantum computation with Kitaev materials.

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“…[76]; see also Refs. [73,74,97] for related earlier applications. The essential role played by proximity-induced superconductivity also becomes clear from this vantage point.…”

Section: Sewing a Non-abelian Spin Liquid To An Electronic Quantumentioning

confidence: 99%

Electrical Probes of the Non-Abelian Spin Liquid in Kitaev Materials

et al. 2020

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“…We will denote the even basis vectors of V ρρ ρ as v 1 and v 2 , so that the odd basis vectors are f v 1 and f v 2 , where the f v i are obtained by acting with f on the bottom leg of the fusion space. Diagrammatically we can denote this vector space by 21 We could have also taken ∆ ρρ…”

Section: Pivotal Structurementioning

confidence: 99%

Fermion condensation and super pivotal categories

Aasen

Lake

Walker

2019

Journal of Mathematical Physics

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We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in the resulting fermionic fusion categories, which we call "m-type" and "q-type" objects. The endomorphism algebras of q-type objects are complex Clifford algebras, and they have no analogues in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations arising from the condensed theories. We prove a series of results relating data in fermionic theories to data in their parent bosonic theories; for example, if C is a modular tensor category containing a fermion, then the tube category constructed from the condensed theory satisfies Tube(C/ψ) ∼ = C × (C/ψ). We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted to three detailed examples of performing fermion condensation to produce fermionic topological phases: we condense fermions in the Ising theory, the SO(3) 6 theory, and the 1 2 E 6 theory, and compute the quasiparticle excitation spectrum in each of the condensed theories. arXiv:1709.01941v2 [cond-mat.str-el]

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“…Gapped boundaries or domain walls (i.e., boundaries between two topological orders) have been widely studied in the literature [71][72][73][74][75][76][77][78][79][80][81][82][83]. One way to describe them is to use the language of "anyon condensation" [80,[84][85][86]: a set of self-bosonic anyons on one side of the boundary/domain wall "condense" into the trivial anyon on the other side.…”

Section: Boundary Of the Double-layer Systemmentioning

confidence: 99%

Folding approach to topological order enriched by mirror symmetry

Jian

Wang

2019

Phys. Rev. B

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We develop a folding approach to study two-dimensional symmetry-enriched topological (SET) phases with the mirror reflection symmetry. Our folding approach significantly transforms the mirror SETs, such that their properties can be conveniently studied through previously known tools:(i) it maps the nonlocal mirror symmetry to an onsite Z 2 layer-exchange symmetry after folding the SET along the mirror axis, so that we can gauge the symmetry; (ii) it maps all mirror SET information into the boundary properties of the folded system, so that they can be studied by the anyon condensation theory-a general theory for studying gapped boundaries of topological orders;and (iii) it makes the mirror anomalies explicitly exposed in the boundary properties, i.e., strictly 2D SETs and those that can only live on the surface of a 3D system can be easily distinguished through the folding approach. With the folding approach, we derive a set of physical constraints on data that describes mirror SET, namely mirror permutation and mirror symmetry fractionalization on the anyon excitations in the topological order. We conjecture that these constraints may be complete, in the sense that all solutions are realizable in physical systems. Several examples are discussed to justify this. Previously known general results on the classification and anomalies are also reproduced through our approach. *

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Fermion condensation and gapped domain walls in topological orders

Cited by 24 publications

References 50 publications

Electrical Probes of the Non-Abelian Spin Liquid in Kitaev Materials

Electrical Probes of the Non-Abelian Spin Liquid in Kitaev Materials

Fermion condensation and super pivotal categories

Folding approach to topological order enriched by mirror symmetry

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