Signatures of broken parity and time-reversal symmetry in generalized string-net models

Lake, Ethan; Wu, Yong‐Shi

doi:10.1103/physrevb.94.115139

Cited by 11 publications

(6 citation statements)

References 55 publications

(134 reference statements)

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“…[33] (see Refs. [31,32,[41][42][43] for such generalizations). In both of these classes of models, it is well understood how to find the ground-state degeneracy [13,44] and the properties of the excitations, such as braiding statistics [13,32,33] (as we will elaborate on shortly).…”

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confidence: 99%

Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview

Huxford¹,

Simon²

2022

Preprint

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In this series of papers, we study a Hamiltonian model for 3+1d topological phases, based on a generalisation of lattice gauge theory known as "higher lattice gauge theory". Higher lattice gauge theory has so called "2-gauge fields" describing the parallel transport of lines, just as ordinary gauge fields describe the parallel transport of points. In the Hamiltonian model this is represented by having labels on the plaquettes of the lattice, as well as the edges. In this paper we summarize our findings in an accessible manner, with more detailed results and proofs to be presented in the other papers in the series. The Hamiltonian model supports both point-like and loop-like excitations, with non-trivial braiding between these excitations. We explicitly construct operators to produce and move these excitations, and use these to find the loop-loop and point-loop braiding relations. These creation operators also reveal that some of the excitations are confined, costing energy to separate. This is discussed in the context of condensation/confinement transitions between different cases of this model. We also discuss the topological charges of the model and use explicit measurement operators to re-derive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the model on the 3-torus. From these measurement operators, we can see that the ground state degeneracy on the 3-torus is related to the number of types of linked loop-like excitations.

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Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview

Huxford¹,

Simon²

2022

Preprint

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“…In particular, since braiding processes which exchange two quasiparticles are odd under reflection, we can impose the constraint that θ P(a),P(b) = θ * a,b , where P(α) is the image of α under reflection and θ a,b is the mutual statistics of the quasiparticles associated with the electric and magnetic cochains a and b 13 . Since we restrict ourselves to Z N reflection-symmetric topological order, we can take θ a,b = exp(2πiab/N ) 36,37 , which means that the action of reflection must permute the quasiparticles in the system, since it must act as "charge conjugation" for either the electric or magnetic sector in order to satisfy P(a)P(b) = −ab. For concreteness, we adopt the choice that reflection acts as charge conjugation on the magnetic sector, so that P(a) = a and…”

Section: Testing For Anomalies and Classifying Fractionalization Patt...mentioning

confidence: 99%

Anomalies and symmetry fractionalization in reflection-symmetric topological order

Lake

2016

Phys. Rev. B

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One of the central ideas regarding anomalies in topological phases of matter is that they imply the existence of higher-dimensional physics, with an anomaly in a D-dimensional theory typically being cancelled by a bulk (D+1)-dimensional symmetry-protected topological phase (SPT). We demonstrate that for some topological phases with reflection symmetry, anomalies may actually be cancelled by a D-dimensional SPT, provided that it comes embedded in an otherwise trivial (D+1)-dimensional bulk. We illustrate this for the example of ZN topological order enriched with reflection symmetry in (2+1)D, and along the way establish a classification of anomalous reflection symmetry fractionalization patterns. In particular, we show that anomalies occur if and only if both electric and magnetic quasiparticle excitations possess nontrivial fractional reflection quantum numbers.

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“…Ever since their conception, the string-net models as originally proposed by Levin and Wen [1] and their subsequent generalizations [2][3][4][5][6][7] have provided a rich playground for studying microscopic realisations of non-chiral topologically ordered phases of matter in 2+1 dimensions. Taking a unitary fusion category (UFC) D [8] as input, these exactly solvable models allow for the explicit realization of several key features of topologically ordered systems, such as ground state degeneracies that depend on the topology of the space and anyonic quasi-particle excitations that satisfy non-trivial braiding statistics.…”

Section: Introductionmentioning

confidence: 99%

Mapping between Morita equivalent string-net states with a constant depth quantum circuit

Lootens,

Cuiper,

Schuch

et al. 2021

Preprint

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We construct a constant depth quantum circuit that maps between Morita equivalent string-net models. Due to its constant depth and unitarity, the circuit cannot alter the topological order, which demonstrates that Morita equivalent string-nets are in the same phase. The circuit is constructed from an invertible bimodule category connecting the two input fusion categories of the relevant string-net models, acting as a generalized Fourier transform for fusion categories. The circuit does not only act on the ground state subspace, but acts unitarily on the full Hilbert space when supplemented with ancillas.

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Signatures of broken parity and time-reversal symmetry in generalized string-net models

Cited by 11 publications

References 55 publications

Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview

Excitations in the Higher Lattice Gauge Theory Model for Topological Phases I: Overview

Anomalies and symmetry fractionalization in reflection-symmetric topological order

Mapping between Morita equivalent string-net states with a constant depth quantum circuit

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