Ising anyons in frustration-free Majorana-dimer models

Ware, Brayden; Son, Jun Ho; Cheng, Meng; Mishmash, Ryan V.; Alicea, Jason; Bauer, Bela

doi:10.1103/physrevb.94.115127

Cited by 43 publications

(59 citation statements)

References 76 publications

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“…I, commutingprojector Hamiltonians for such 2D phases have also been found in Refs. [18,41,42]. Θ 1;2 ¼ π/2 translates into the fractional exchange statistics of symmetry fluxes in the 2D FSPT phase, which as proven in Ref.…”

Section: Physical Picturementioning

confidence: 70%

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

2018

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We study Abelian braiding statistics of loop excitations in three-dimensional gauge theories with fermionic particles and the closely related problem of classifying 3D fermionic symmetry-protected topological (FSPT) phases with unitary symmetries. It is known that the two problems are related by turning FSPT phases into gauge theories through gauging the global symmetry of the former. We show that there exist certain types of Abelian loop braiding statistics that are allowed only in the presence of fermionic particles, which correspond to 3D "intrinsic" FSPT phases, i.e., those that do not stem from bosonic SPT phases. While such intrinsic FSPT phases are ubiquitous in 2D systems and in 3D systems with antiunitary symmetries, their existence in 3D systems with unitary symmetries was not confirmed previously due to the fact that strong interaction is necessary to realize them. We show that the simplest unitary symmetry to support 3D intrinsic FSPT phases is Z 2 × Z 4 . To establish the results, we first derive a complete set of physical constraints on Abelian loop braiding statistics. Solving the constraints, we obtain all possible Abelian loop braiding statistics in 3D gauge theories, including those that correspond to intrinsic FSPT phases. Then, we construct exactly soluble state-sum models to realize the loop braiding statistics. These state-sum models generalize the well-known Crane-Yetter and Dijkgraaf-Witten models.

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Section: Physical Picturementioning

confidence: 70%

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

2018

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“…There is an apparent similarity between our dimensional reduction procedures and the decorated domain wall methods [44,45,46,47]. One should consider dimensional reduction as a probe of a phase or anomaly, while decorated domain walls are a method to construct them.…”

Section: Discussionmentioning

confidence: 99%

Anomaly matching in the symmetry broken phase: Domain walls, CPT, and the Smith isomorphism

2020

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Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is spontaneously broken, for the continuous case, the anomaly implies low-energy theorems about certain couplings of the Goldstone modes. Here we study the case of spontaneously broken discrete symmetries, such as Z2 and T . Symmetry breaking leads to domain walls, and the physics of the domain walls is constrained by the anomaly. We investigate how the physics of the domain walls leads to a matching of the original discrete anomaly. We analyze the symmetry structure on the domain wall, which requires a careful analysis of some properties of the unbreakable CP T symmetry. We demonstrate the general results on some examples and we explain in detail the mod 4 periodic structure that arises in the Z2 and T case. This gives a physical interpretation for the Smith isomorphism, which we also extend to more general abelian groups. We show that via symmetry breaking and the analysis of the physics on the wall, the computations of certain discrete anomalies are greatly simplified. Using these results we perform new consistency checks on the infrared phases of 2 + 1 dimensional QCD. * which by construction leaves the boundary conditions invariant and therefore indeed acts on the wall! But observe that this is an anti-unitary symmetry, since CP ⊥ T is anti-unitary. Thus, the correct answer to the question about the fate of the spontaneously broken, unitary, Z 2 symmetry is that it becomes some anti-unitary symmetry acting on the wall.By the same argument, if we began with a spontaneously broken anti-unitary Z 2 symmetry, the domain wall would inherit a unitary Z 2 symmetry. In fact, we will derive a 4-periodic dimensional

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“…[34] studied certain special cases of simple-current fermion condensation, such as when the condensed self-fermion fuses with itself into the trivial sector, which generates a Z 2 1-form global symmetry. Proposals of simple-current fermion condensation on the boundaries of certain simple systems have also been made, e.g., in quantum spin liquid [35], and in Ising topological order [36,37]. Ref.…”

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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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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Ising anyons in frustration-free Majorana-dimer models

Cited by 43 publications

References 76 publications

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions

Anomaly matching in the symmetry broken phase: Domain walls, CPT, and the Smith isomorphism

Fermion condensation and gapped domain walls in topological orders

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