Bosonic topological phases of matter: Bulk-boundary correspondence, symmetry protected topological invariants, and gauging

Tiwari, Apoorv; Chen, Xiao; Shiozaki, Ken; Ryu, Shinsei

doi:10.1103/physrevb.97.245133

Cited by 26 publications

(31 citation statements)

References 116 publications

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“…Indeed, similar to (2+1)d abelian DW theories, (3+1)d DW are constructed from three kinds of cocycles which we call type-(II),(III),(IV). The topological action corresponding to type-(II),(III) takes the form [36,42] S (II,III)|SPT (M) ∝ Surface theories corresponding to these anomalies can be constructed via the above recipe by choosing α(g) ∝ g dg or α(g) ∝ g g g with the appropriate coefficient in (34).…”

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

confidence: 99%

“…In comparison much less is known in (3+1)d. The only known classes of TQFTs with intrinsic topological order 2 are topological gauge theories built from groups or group-like structures. There has been significant recent progress in the study of such theories [19,23,[35][36][37][38][39][40][41][42][43][44]. Another class of (3+1)d theories uses unitary braided fusion categories as the input.…”

Section: Introductionmentioning

confidence: 99%

“…In fact gauging the global symmetry G in an SPT labeled by [ω] yields the Dijkgraaf-Witten model (G, [ω]). Furthermore, one notices that SPT topological invariants are the U(1)valued response functions that an SPT furnishes in the presence of a background G-bundle [42,[69][70][71][72][73].…”

Section: Introductionmentioning

confidence: 99%

“…Gauging a 1-form symmetry is synonymous to condensing abelian lines that generate the symmetry. If the lines are all bosonic and mutually transparent, they can be condensed and there is no 1-form 't Hooft anomaly[31,101].…”

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confidence: 99%

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

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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From gauge to higher gauge models of topological phases

Delcamp

Tiwari

2018

J. High Energ. Phys.

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“…From fermionic Chern arguments, one would expect to always find an even number of photonic edge states -but this is not the case [45][46][47][48]. Although a widely held belief, the conventional bulk-boundary correspondence fails for spin-1 bosons [76].…”

Section: Does This Mass Have Any Physical Origin?mentioning

confidence: 99%

Photonic Dirac monopoles and skyrmions: spin-1 quantization [Invited]

Mechelen¹,

Jacob²

2018

Opt. Mater. Express

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We introduce the concept of a photonic Dirac monopole, appropriate for photonic crystals, metamaterials and 2D materials, by utilizing the Dirac-Maxwell correspondence. We start by exploring vacuum where the reciprocal momentum space of both Maxwell's equations and the massless Dirac equation (Weyl equation) possess a magnetic monopole. The critical distinction is the nature of magnetic monopole charges, which are integer valued for photons but half-integer for electrons. This inherent difference is directly tied to the spin and ultimately connects to the bosonic or fermionic behavior. We also show the presence of photonic Dirac strings, which are line singularities in the underlying Berry gauge potential. While the results in vacuum are intuitively expected, our central result is the application of this topological Dirac-Maxwell correspondence to 2D photonic (bosonic) materials, as opposed to conventional electronic (fermionic) materials. Intriguingly, within dispersive matter, the presence of photonic Dirac monopoles is captured by nonlocal quantum Hall conductivity -i.e. a spatiotemporally dispersive gyroelectric constant. For both 2D photonic and electronic media, the nontrivial topological phases emerge in the context of massive particles with broken time-reversal symmetry. However, the bulk dynamics of these bosonic and fermionic Chern insulators are characterized by spin-1 and spin-1 ⁄2 skyrmions in momentum space, which have fundamentally different interpretations. This is exemplified by their contrasting spin-1 and spin-1 ⁄2 helically quantized edge states. Our work sheds light on the recently proposed quantum gyroelectric phase of matter and the essential role of photon spin quantization in topological bosonic phases. * zjacob@purdue.edu arXiv:1806.09879v3 [physics.optics]

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Orbifold groupoids

Gaiotto

Kulp

2021

J. High Energ. Phys.

102

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We review the properties of orbifold operations on two-dimensional quantum field theories, either bosonic or fermionic, and describe the “Orbifold groupoids” which control the composition of orbifold operations. Three-dimensional TQFT’s of Dijkgraaf-Witten type will play an important role in the analysis. We briefly discuss the extension to generalized symmetries and applications to constrain RG flows.

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Bosonic topological phases of matter: Bulk-boundary correspondence, symmetry protected topological invariants, and gauging

Abstract: A. Group cohomology for finite abelian groups 23 B. Orbifolding with discrete torsion and relation to 1 + 1d SPTs 23 C. SPT response theory and group cocycles 24 D. Quantization of 2 + 1d surface theory 26 References 27 arXiv:1710.04730v1 [cond-mat.str-el]

Cited by 26 publications

References 116 publications

From gauge to higher gauge models of topological phases

From gauge to higher gauge models of topological phases

Photonic Dirac monopoles and skyrmions: spin-1 quantization [Invited]

Orbifold groupoids

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