Linking Numbers, Spin, and Statistics of Solitons

Wilczek, Frank; Zee, A.

doi:10.1103/physrevlett.51.2250

Cited by 770 publications

(560 citation statements)

References 15 publications

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“…For a simple topological derivation that holds both relativistically and nonrelativistically, see Ref. 50. In Abelian Chern-Simons gauge theories, as well as in related CFTs, the statistics of the quasiparticles, as well as their spins, are quadratic expressions in their quantum numbers (the fluxes in the dynamical gauge fields).…”

Section: Discussionmentioning

confidence: 99%

Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

Bradlyn

Read

2015

Phys. Rev. B

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We show that the topological central charge of a topological phase can be directly accessed from the ground-state wavefunctions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to addition of another topological invariant that arises in some cases. For trial wavefunctions that are given by conformal blocks (chiral correlation functions) in a conformal field theory (CFT), we carry out this calculation analytically, using the hypothesis of generalized screening. The topological central charge is found to be that of the underlying CFT used in the construction, as expected. The calculation makes use of the gravitational anomaly in the chiral CFT. It is also shown that the Hall conductivity can be obtained in an analogous way from the U(1) gauge anomaly.

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Section: Discussionmentioning

confidence: 99%

Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

Bradlyn

Read

2015

Phys. Rev. B

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“…Chern-Simons gauge theories coupled to scalar matter field also support the soliton solutions carrying fractional angular momentum [5,6]. An example which provides static multi-soliton solutions is relativistic Chern-Simons Higgs model of a specific φ 6 scalar potential, and it admits both topological and nontopological solitons [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Gravitating Self-Dual Chern–Simons Solitons

Chung

Kim³

et al. 2001

Annals of Physics

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Self-dual solitons of Chern-Simons Higgs theory are examined in curved spacetime. We derive duality transformation of the Einstein Chern-Simons Higgs theory within path integral formalism and study various aspects of dual formulation including derivation of Bogomolnyi type bound. We find all possible rotationally-symmetric soliton configurations carrying magnetic flux and angular momentum when underlying spatial manifolds of these objects comprise a cone, a cylinder, and a two sphere.

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“…In addition, following an argument used by Wilczek and Zee in Ref. 50 in their analysis of solitons in the O(3) NLSM with Hopf term, our result implies that a bound state of a vortex in b 1 and a vortex in b 2 carries intrinsic angular momentum J = θ 2π . When θ = π, we have J = 1 2 , which means that the bound state is a fermion.…”

Section: Spectrum Of Chargesmentioning

confidence: 94%

“…Then we must have 50) in order for the commutation relations to be invariant under conjugation by T . Now suppose we have a state |Ψ of the system which is time-reversal invariant, i.e., T |Ψ = |Ψ .…”

Section: Interspecies Tunnelingmentioning

confidence: 99%

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Bosonic analog of a topological Dirac semimetal: Effective theory, neighboring phases, and wire construction

2016

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We construct a bosonic analog of a two-dimensional topological Dirac Semi-Metal (DSM). The low-energy description of the most basic 2D DSM model consists of two Dirac cones at positions ±k0 in momentum space. The local stability of the Dirac cones is guaranteed by a composite symmetry Z T I 2 , where T is timereversal and I is inversion. This model also exhibits interesting time-reversal and inversion symmetry breaking electromagnetic responses. In this work we construct a bosonic version by replacing each Dirac cone with a copy of the O(4) Nonlinear Sigma Model (NLSM) with topological theta term and theta angle θ = ±π. One copy of this NLSM also describes the gapless surface termination of the 3D Bosonic Topological Insulator (BTI). We compute the time-reversal and inversion symmetry breaking electromagnetic responses for our model and show that they are twice the value one gets in the DSM case matching what one might expect from, for example, a bosonic Chern insulator. We also investigate the stability of the BSM model and find that the composite Z T I 2 symmetry again plays an important role. Along the way we clarify many aspects of the surface theory of the BTI including the electromagnetic response, the charges and statistics of vortex excitations, and the stability to symmetry-allowed perturbations. We briefly comment on the relation between the various descriptions of the O(4) NLSM with θ = π used in this paper (a dual vortex description and a description in terms of four massless fermions) and the recently proposed dual description of the BTI surface in terms of 2 + 1 dimensional Quantum Electrodynamics with two flavors of fermion (N = 2 QED3). In a set of four Appendixes we review some of the tools used in the paper, and also derive some of the more technical results.

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Linking Numbers, Spin, and Statistics of Solitons

Cited by 770 publications

References 15 publications

Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

Gravitating Self-Dual Chern–Simons Solitons

Bosonic analog of a topological Dirac semimetal: Effective theory, neighboring phases, and wire construction

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