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F. A. Bais

Publications and source records attributed to F. A. Bais.

At least 19 recordsLinked to original sources
arXiv2014

Diagrammatics for Bose condensation in anyon theories

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs). These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase, such that they can be evaluated using the data of the original theory and a limited number of VLCs. Some representative examples are worked out in detail.

cond-mat.str-el↗
arXiv2014

Topological symmetry breaking: Domain walls and partial instability of chiral edges

In 2D topological systems chiral edges may exhibit a spectral change due to the formation of a Bose condensate and partial confinement in the bulk according to the topological symmetry breaking (TSB) mechanism. We analyze in detail what happens in the bulk as well as on the edge for a set of simple chiral fractional quantum Hall systems. TSB corresponds to the spontaneous breaking of a global discrete symmetry and therefore to the appearance of domain walls in the bulk and kinks on the edge. The walls are locally metastable and break if a confined particle-hole pair is created.

cond-mat.str-el↗
arXiv2014

Noncompact dynamical symmetry of a spin-orbit coupled oscillator

We explain the finite as well as infinite degeneracy in the spectrum of a particular system of spin-1/2 fermions with spin-orbit coupling in three spatial dimensions. Starting from a generalized Runge-Lenz vector, we explicitly construct a complete set of symmetry operators, which span a noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only involves a particular, infinite, so called singleton representation. In the branch where orbital and spin angular momentum are aligned the full representation appears, constituting a 3D analogue of Landau levels. Anti-aligning the spin leads to a finite degeneracy due to a truncation of the singleton representation. We conclude the paper by constructing the spectrum generating algebra of the problem.

cond-mat.mes-hall↗
arXiv2012

The modular S-matrix as order parameter for topological phase transitions

We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular $S$-matrix, also in the broken phase. From the measured broken $S$-matrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular $S$-matrix can be employed as a matrix valued non-local order parameter from which the low-energy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions we studied a non-abelian anyon model based on the quaternion group $H=\bar{D_2}$ of order eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established.

cond-mat.mes-hall↗
arXiv2010

Towards a non-abelian electric-magnetic symmetry: the skeleton group

We propose an electric-magnetic symmetry group in non-abelian gauge theory, which we call the skeleton group. We work in the context of non-abelian unbroken gauge symmetry, and provide evidence for our proposal by relating the representation theory of the skeleton group to the labelling and fusion rules of charge sectors. We show that the labels of electric, magnetic and dyonic sectors in non-abelian Yang-Mills theory can be interpreted in terms of irreducible representations of the skeleton group. Decomposing tensor products of these representations thus gives a set of fusion rules which contain information about the full fusion rules of these charge sectors. We demonstrate consistency of the skeleton's fusion rules with the known fusion rules of the purely electric and purely magnetic magnetic sectors, and extract new predictions for the fusion rules of dyonic sectors in particular cases. We also implement S-duality and show that the fusion rules obtained from the skeleton group commute with S-duality.

hep-th↗
arXiv2010

Topological entanglement entropy relations for multi phase systems with interfaces

We study the change in topological entanglement entropy that occurs when a two-dimensional system in a topologically ordered phase undergoes a transition to another such phase due to the formation of a Bose condensate. We also consider the topological entanglement entropy of systems with domains in different topological phases, and of phase boundaries between these domains. We calculate the topological entropy of these interfaces and derive two fundamental relations between the interface topological entropy and the bulk topological entropies on both sides of the interface.

cond-mat.str-el↗
arXiv2008

A theory of topological edges and domain walls

We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on topological symmetry breaking that we have introduced and presented elsewhere. After summarizing the method, we work out predictions for the spectrum of edge excitations and for the transport through edges in some representative examples. These include domain walls between the Abelian and non-Abelian topological phases of Kitaev's honeycomb lattice model in a magnetic field, as well as recently proposed domain walls between spin polarized and unpolarized non-Abelian fractional quantum Hall states at different filling fractions.

cond-mat.mes-hall↗
arXiv2008

Anyonic order parameters for discrete gauge theories on the lattice

We present a new family of gauge invariant non-local order parameters for (non-abelian) discrete gauge theories on a Euclidean lattice, which are in one-to-one correspondence with the excitation spectrum that follows from the representation theory of the quantum double D(H) of the finite group H. These combine magnetic flux-sector labeled by a conjugacy class with an electric representation of the centralizer subgroup that commutes with the flux. In particular cases like the trivial class for magnetic flux, or the trivial irrep for electric charge, these order parameters reduce to the familiar Wilson and the 't Hooft operators respectively. It is pointed out that these novel operators are crucial for probing the phase structure of a class of discrete lattice models we define, using Monte Carlo simulations.

cond-mat.mes-hall↗
arXiv2008

Condensate induced transitions between topologically ordered phases

We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetry breaking phase transitions which applies to phases with topological excitations described by quantum groups or modular tensor categories. This enables us to deal with phases whose quasiparticles have non-integer quantum dimensions and obey braid statistics. Many examples of such phases can be constructed from two-dimensional rational conformal field theories and we find that there is a beautiful connection between quantum group symmetry breaking and certain well-known constructions in conformal field theory, notably the coset construction, the construction of orbifold models and more general conformal extensions. Besides the general framework, many representative examples are worked out in detail.

cond-mat.mes-hall↗
arXiv2008

Magnetic Charge Lattices, Moduli Spaces and Fusion Rules

We analyze the set of magnetic charges carried by smooth BPS monopoles in Yang-Mills-Higgs theory with arbitrary gauge group G spontaneously broken to a subgroup H. The charges are restricted by a generalized Dirac quantization condition and by an inequality due to Murray. Geometrically, the set of allowed charges is a solid cone in the coroot lattice of G, which we call the Murray cone. We argue that magnetic charge sectors correspond to points in the Murray cone divided by the Weyl group of H; hence magnetic charge sectors are labelled by dominant integral weights of the dual group H*. We define generators of the Murray cone modulo Weyl group, and interpret the monopoles in the associated magnetic charge sectors as basic; monopoles in sectors with decomposable charges are interpreted as composite configurations. This interpretation is supported by the dimensionality of the moduli spaces associated to the magnetic charges and by classical fusion properties for smooth monopoles in particular cases. Throughout the paper we compare our findings with corresponding results for singular monopoles recently obtained by Kapustin and Witten.

hep-th↗
arXiv2006

The breaking of quantum double symmetries by defect condensation

In this paper, we study the phenomenon of Hopf or more specifically quantum double symmetry breaking. We devise a criterion for this type of symmetry breaking which is more general than the one existing in the literature, and therefore extends the number of possible breaking patterns that can be described consistently. We start by recalling why the extended symmetry notion of quantum double algebras is an optimal tool when analyzing a wide variety of two dimensional physical systems including quantum fluids, crystals and liquid crystals. The power of this approach stems from the fact that one may characterize both ordinary and topological modes as representations of a single (generally non-Abelian) Hopf symmetry. In principle a full classification of defect mediated as well as ordinary symmetry breaking patterns and subsequent confinement phenomena can be given. The formalism applies equally well to systems exhibiting global, local, internal and/or external (i.e. spatial) symmetries. The subtle differences in interpretation for the various situations are pointed out. We show that the Hopf symmetry breaking formalism reproduces the known results for ordinary (electric) condensates, and we derive formulae for defect (magnetic) condensates which also involve the phenomenon of symmetry restoration. These results are applied in two papers which will be published in parallel.

cond-mat.mes-hall↗
arXiv2006

Defect mediated melting and the breaking of quantum double symmetries

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.

cond-mat.mes-hall↗
arXiv2006

Nematic phases and the breaking of double symmetries

In this paper we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e. as representations of a single (non-Abelian) Hopf symmetry. The method that exists in the literature (and is developed in a paper published in parallel) allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra and the symmetry algebra characterizing the effective ``low energy'' theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two dimensional quantum fluids, crystals and liquid crystals.

cond-mat.mes-hall↗
arXiv2003

More on core instabilities of magnetic monopoles

In this paper we present new results on the core instability of the 't Hooft Polyakov monopoles we reported on before. This instability, where the spherical core decays in a toroidal one, typically occurs in models in which charge conjugation is gauged. In this paper we also discuss a third conceivable configuration denoted as ``split core'', which brings us to some details of the numerical methods we employed. We argue that a core instability of 't Hooft Polyakov type monopoles is quite a generic feature of models with charged Higgs particles.

hep-th↗
arXiv2003

Charge instabilities due to local charge conjugation symmetry in (2+1)-dimensions

Alice electrodynamics (AED) is a theory of electrodynamics in which charge conjugation is a local gauge symmetry. In this paper we investigate a charge instability in alice electrodynamics in (2+1)-dimensions due to this local charge conjugation. The instability manifests itself through the creation of a pair of alice fluxes. The final state is one in which the charge is completely delocalized, i.e., it is carried as cheshire charge by the flux pair that gets infinitely separated. We determine the decay rate in terms of the parameters of the model. The relation of this phenomenon with other salient features of 2-dimensional compact QED, such as linear confinement due to instantons/monopoles, is discussed.

hep-th↗
arXiv2003

Dynamical vacuum selection in field theories with flat directions in their potential

In this paper we show that in field theories with topologically stable kinks and flat directions in their potential, a so-called dynamical vacuum selection (DVS) takes place in the non-trivial, soliton sector of the theory. We explore this DVS mechanism using a specific model. For this model we show that there is only a static kink solution when very specific boundary conditions are met, very similar to the case of vortices in two dimensions. In the case of other boundary conditions a scalar cloud is expelled to infinity, leaving a static kink behind. Other circumstances under which DVS may or may not take place are discussed as well.

hep-th↗
arXiv2002

Simulations of Alice Electrodynamics on a Lattice

In this paper we present results of numerical simulations and some (analytical) approximations of a compact $U(1)\ltimes\ZZ_2$ lattice gauge theory, including an extra bare mass term for Alice fluxes. The subtle interplay between Alice fluxes and (Cheshire) magnetic charges is analysed. We determine the phase diagram and some characteristics of the model in three and four dimensions. The results of the numerical simulations in various regimes, compare well with some analytic approximations.

hep-lat↗