Landau-Ginzburg theories of non-Abelian quantum Hall states from non-Abelian bosonization

Abstract

It is an important open problem to understand the landscape of non-Abelian fractional quantum Hall phases which can be obtained starting from physically motivated theories of Abelian composite particles. We show that progress on this problem can be made using recently proposed non-Abelian bosonization dualities in 2+1 dimensions, which morally relate U (N ) k and SU (k) −N Chern-Simons-matter theories. The advantage of these dualities is that regions of the phase diagram which may be obscure on one side of the duality can be accessed by condensing local operators on the other side. Starting from parent Abelian states, we use this approach to construct Landau-Ginzburg theories of non-Abelian states through a pairing mechanism. In particular, we obtain the bosonic Read-Rezayi sequence at fillings ν = k/(kM + 2) by starting from k layers of bosons at ν = 1/2 with M Abelian fluxes attached. The Read-Rezayi states arise when k-clusters of the dual non-Abelian bosons condense. We extend this construction by showing that N f -component generalizations of the Halperin (2, 2, 1) bosonic states have dual descriptions in terms of SU (N f + 1) 1 Chern-Simons-matter theories, revealing an emergent global symmetry in the process. Clustering k layers of these theories yields a non-Abelian SU (N f )-singlet state at filling ν = kN f /(N f + 1 + kM N f ).ψ ↔ φ These authors contributed equally to the development of this work.Recent progress in the study of non-Abelian Chern-Simons-matter theories in their large-Using the non-Abelian bosonization dualities, we construct LG theories of the full bosonic RR sequence at filling fractions ν = k/(kM + 2), k, M ∈ Z, which do not suffer from these problems. These theories are obtained by starting with k layers of ν = 1/2 bosonic QH

Universal low-temperature behavior of two-dimensional lattice scalar chromodynamics

“…To perform the correct universality check for N f = 2, as discussed in detail in Ref. [8], it is important to consider a Binder parameter in the SU(2) gauge theory that maps onto the usual vector O(5) Binder parameter under the isomorphism Sp(N 2 )/Z 2 → SO (5). The Binder parameter U defined in Eq.…”

“…More recently, it has been pointed out that they may also characterize emerging phenomena in condensed-matter physics, see, e.g., Refs. [2][3][4][5][6] and references therein. As a consequence, the large-scale properties of gauge models are also of interest in two or three dimensions.…”

Two-dimensional multicomponent Abelian-Higgs lattice models

“…Models of complex scalar matter fields with abelian and nonabelian gauge symmetries effectively emerge in several interesting systems, such as superconductors and superfluids, quantum Hall states, quantum SU(N ) antiferromagnets, unconventional quantum phase transitions, etc., see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12] and references therein. Among the paradigmatic models considered, an important role is played by the multicomponent lattice Abelian-Higgs (AH) model or lattice scalar electrodynamics, which is a lattice U(1) gauge theory coupled with an N -component complex scalar field, characterized by a global SU(N ) symmetry.…”

Phase Diagram, Symmetry Breaking, and Critical Behavior of Three-Dimensional Lattice Multiflavor Scalar Chromodynamics

“…The large-scale properties of three-dimensional (3D) gauge models and the nature of their thermal or quantum transitions are of interest in several physical contexts. For instance, they are relevant for superconductivity [3], for topological order and quantum transitions [4][5][6][7][8], and also in highenergy physics, as they describe the finite-temperature electroweak and strong-interaction transition which occurred in the early universe [9] and which is presently being investigated in heavy-ion collisions [10].…”