State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter

Bhardwaj, Lakshya; Gaiotto, Davide; Kapustin, Anton

doi:10.1007/jhep04(2017)096

Cited by 130 publications

(245 citation statements)

References 56 publications

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“…On the other hand, the GDW picture makes perfect sense for discussing about selffermion condensation. We just need to consider a GDW between a bTO and a fermionic topological order (fTO) [31][32][33], whose fundamental degrees of freedom are fermions (figure 1(b)). From the GDW picture of self-boson condensation, we expect that a self-fermion condensation has the following properties: (1) all excitation in F can pass through the wall and become some excitations in B; (2) the condensed self-fermions in B becomes local fermions in F when they pass through the wall; (3) certain anyons in B cannot pass through the wall.…”

Section: Jhep03(2017)172mentioning

confidence: 99%

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Fermion condensation and gapped domain walls in topological orders

Wan¹,

Wang²

2017

J. High Energ. Phys.

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Abstract:We study fermion condensation in bosonic topological orders in two spatial dimensions. Fermion condensation may be realized as gapped domain walls between bosonic and fermionic topological orders, which may be thought of as real-space phase transitions from bosonic to fermionic topological orders. This picture generalizes the previous idea of understanding boson condensation as gapped domain walls between bosonic topological orders. While simple-current fermion condensation was considered before, we systematically study general fermion condensation and show that it obeys a Hierarchy Principle: a general fermion condensation can always be decomposed into a boson condensation followed by a minimal fermion condensation. The latter involves only a single self-fermion that is its own anti-particle and that has unit quantum dimension. We develop the rules of minimal fermion condensation, which together with the known rules of boson condensation, provides a full set of rules for general fermion condensation.

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Section: Jhep03(2017)172mentioning

confidence: 99%

“…Ref. [33] also studied fermionic boundary condition of Z 2 -toric code. In this work, we consider general fermion condensation, i.e., condensing fermions of arbitrary quantum dimensions, in the context of GDWs between bTOs and fTOs.…”

Section: Jhep03(2017)172mentioning

confidence: 99%

Fermion condensation and gapped domain walls in topological orders

Wan¹,

Wang²

2017

J. High Energ. Phys.

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“…A for more details). This obviously reminds of the super-cohomology appearing in fermionic topological orders [31,89].…”

Section: Generalizationsmentioning

confidence: 81%

“…where we have introduced background fields g ∈ Hom(π 1 (M), G) andĥ ∈ H 2 (M,Ĥ) 31 . α(g) ∈ Z 3 (M, H) refers to the cocycle α evaluated on g. The background fieldĥ enters the action via the coupling N h ĥ ,…”

Section: Scenario 4: Anomalies From Gauging 1-form Subgroup Of 2-gmentioning

confidence: 99%

From gauge to higher gauge models of topological phases

Delcamp

Tiwari

2018

J. High Energ. Phys.

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We consider exactly solvable models in (3+1)d whose ground states are described by topological lattice gauge theories. Using simplicial arguments, we emphasize how the consistency condition of the unitary map performing a local change of triangulation is equivalent to the coherence relation of the pentagonator 2-morphism of a monoidal 2-category. By weakening some axioms of such 2-category, we obtain a cohomological model whose underlying 1-category is a 2-group. Topological models from 2-groups together with their lattice realization are then studied from a higher gauge theory point of view. Symmetry protected topological phases protected by higher symmetry structures are explicitly constructed, and the gauging procedure which yields the corresponding topological gauge theories is discussed in detail. We finally study the correspondence between symmetry protected topological phases and 't Hooft anomalies in the context of these higher group symmetries. CONTENTS

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“…There are already many different ways to construct exactly soluble models to systematically realize topolog- ical orders, SPT orders, and SET orders. 1,30,49,52,67,[71][72][73][74] But it does not hurt to have one more construction. In this paper, we will construct some simple toy models with higher symmetry that realize some topological orders, SET orders, and SPT orders.…”

Section: F the Usefulness Of Higher Symmetry In Condensed Mattermentioning

confidence: 99%

Emergent anomalous higher symmetries from topological order and from dynamical electromagnetic field in condensed matter systems

Wen

2019

Phys. Rev. B

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IX. Lattice models that realize higher SPT phasessystematic constructions 21 A. Models realizing bosonic SPT phases 21 B. Models realizing bosonic higher SPT phases 21 C. More general bosonic hSPT phases 22 D. Fermionic hSPT phases 23 E. The usefulness of hSPT phases 24 X. Lattice models that realize topological orders with higher symmetry 24 A. The first type of constructions 24 B. The second type of constructions 24 XI. EM condensed matter systems and their higher symmetry 25 A. Space-time complex, cochains, and cocycles 27 B. Path integral and Hamiltonian 30 References 31 arXiv:1812.02517v5 [cond-mat.str-el] 21 Apr 2019 R/Z J− a R/Z J ) e i 2π B 3 I≤J k IJ a R/Z I ( da R/Z J − da R/Z J )− da R/Z I a R/Z J e − B 3 I R/Z J − da R/Z J )− da R/Z I a R/Z J = e i 2π M 4 k IJ ( da R/Z I − da R/Z I )( da R/Z J − da R/Z J R/Z I )( da R/Z J − da R/Z J ) = e − i 2π M 4 I,J K IJ a R/Z I d da R/Z J , (81) where d da R/Z J can be viewed as the Poincaré dual of the worldline of the U (1) monoples. This implies that the effect of the topological term e i 2π M 4 I≤J k IJ ( da R/Z I − da R/Z I )( da R/Z J − da R/Z J

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State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter

Cited by 130 publications

References 56 publications

Fermion condensation and gapped domain walls in topological orders

Fermion condensation and gapped domain walls in topological orders

From gauge to higher gauge models of topological phases

Emergent anomalous higher symmetries from topological order and from dynamical electromagnetic field in condensed matter systems

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