Model of fractionalization of Faraday lines in compact electrodynamics

Geraedts, Scott D.; Motrunich, Olexei I.

doi:10.1103/physrevb.90.214505

Cited by 6 publications

(11 citation statements)

References 14 publications

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“…Similar considerations of fractionalized line-charges in 3+1-dimensions appeared in Ref. [147]. Phases with disordered rotors {θ i } are characterized by Higgs condensates of the vortices J and a /2π that break the dual gauge symmetry.…”

Section: Dual Formulation and Fractionalized Chargesmentioning

confidence: 80%

Dual gauge field theory of quantum liquid crystals in two dimensions

et al. 2017

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We present a self-contained review of the theory of dislocation-mediated quantum melting at zero temperature in two spatial dimensions. The theory describes the liquid-crystalline phases with spatial symmetries in between a quantum crystalline solid and an isotropic superfluid: quantum nematics and smectics. It is based on an Abelian-Higgs-type duality mapping of phonons onto gauge bosons ("stress photons"), which encode for the capacity of the crystal to propagate stresses. Dislocations and disclinations, the topological defects of the crystal, are sources for the gauge fields and the melting of the crystal can be understood as the proliferation (condensation) of these defects, giving rise to the Anderson-Higgs mechanism on the dual side. For the liquid crystal phases, the shear sector of the gauge bosons becomes massive signaling that shear rigidity is lost. After providing the necessary background knowledge, including the order parameter theory of two-dimensional quantum liquid crystals and the dual theory of stress gauge bosons in bosonic crystals, the theory of melting is developed step-by-step via the disorder theory of dislocation-mediated melting. Resting on symmetry principles, we derive the phenomenological imaginary time actions of quantum nematics and smectics and analyze the full spectrum of collective modes. The quantum nematic is a superfluid having a true rotational Goldstone mode due to rotational symmetry breaking, and the origin of this 'deconfined' mode is traced back to the crystalline phase. The two-dimensional quantum smectic turns out to be a dizzyingly anisotropic phase with the collective modes interpolating between the solid and nematic in a non-trivial way. We also consider electrically charged bosonic crystals and liquid crystals, and carefully analyze the electromagnetic response of the quantum liquid crystal phases. In particular, the quantum nematic is a real superconductor and shows the Meissner effect. Their special properties inherited from spatial symmetry breaking show up mostly at finite momentum, and should be accessible by momentum-sensitive spectroscopy.

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Section: Dual Formulation and Fractionalized Chargesmentioning

confidence: 80%

Dual gauge field theory of quantum liquid crystals in two dimensions

et al. 2017

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“…Such generalizations have been discussed formally recently [33,[37][38][39], and similar ideas can be useful for constructing explicit models and analyzing physical properties of such phases. As a simple demonstration, in a forthcoming publication, we will consider a lattice CQED model where multiple monopoles condense and lead to a novel topological phase of CQED with fractionalized Faraday lines [34].…”

Section: Discussionmentioning

confidence: 99%

“…The hedgehog has well-defined statistics as it encircles the electric field lines, and we expect it to acquire a phase of 2π=d when this happens around the elementary fractionalized line. The matter fields z ↑ and z ↓ are confined, but still act as sources and sinks for the electric field lines of integer strength; therefore, the line topological excitations in the system are defined only up to an integer, and we can say that the system has Z d topological order [33,34].…”

Section: Realizing Symmetry-enriched Topological Phases By Bindinmentioning

confidence: 99%

“…We argue that when d ¼ 1, these phases are analogs of bosonic symmetry-protected topological phases for such CQED × boson systems and have quantized crosstransverse response given by the integer c. On the other hand, when d > 1, these phases are analogs of bosonic symmetry-enriched topological phases and have fractional cross-transverse response given by a rational number c=d; these phases also feature fractionalized Faraday line excitations of the CQED and fractionalized boson particle excitations, as well as nontrivial mutual statistics between the particle and line excitations [33,34].…”

Section: Appendix: Spt-and Set-like Phases In a Cqed × Boson Model Inmentioning

confidence: 99%

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Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases

Geraedts

Motrunich

2014

Phys. Rev. X

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We study a topological phase of interacting bosons in (3 þ 1) dimensions that is protected by charge conservation and time-reversal symmetry. We present an explicit lattice model that realizes this phase and that can be studied in sign-free Monte Carlo simulations. The idea behind our model is to bind bosons to topological defects called hedgehogs. We determine the phase diagram of the model and identify a phase where such bound states are proliferated. In this phase, we observe a Witten effect in the bulk whereby an external monopole binds half of the elementary boson charge, which confirms that it is a bosonic topological insulator. We also study the boundary between the topological insulator and a trivial insulator. We find a surface phase diagram that includes exotic superfluids, a topologically ordered phase, and a phase with a Hall effect quantized to one-half of the value possible in a purely two-dimensional system. We also present models that realize symmetry-enriched topologically ordered phases by binding multiple hedgehogs to each boson; these phases show charge fractionalization and intrinsic topological order as well as a fractional Witten effect.

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“…In principle, one could also try to find an alternate basis in which all configurations have positive weights. However, this has been possible only in a few interesting cases [34,35], including some models of topologically ordered states of matter [36][37][38].…”

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confidence: 99%

Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

2016

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We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S=1/2 antiferromagnets using the basis of spin eigenstates of clusters to avoid the severe sign problem faced by other QMC methods. We demonstrate the utility of the method in several cases with competing exchange interactions and flag important limitations as well as possible extensions of the method.

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Model of fractionalization of Faraday lines in compact electrodynamics

Cited by 6 publications

References 14 publications

Dual gauge field theory of quantum liquid crystals in two dimensions

Dual gauge field theory of quantum liquid crystals in two dimensions

Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases

Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

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