Spontaneous Symmetry Breaking in the Non-Abelian Anyon Fluid

Abstract

We study the theory of non-relativistic matter with non-Abelian $U(2)$ Chern-Simons gauge interaction in $(2+1)$ dimensions. We adopt the mean field approximation in the current-algebra formulation already applied to the Abelian anyons. We first show that this method is able to describe both ``boson-based'' and ``fermion-based'' anyons and yields consistent results over the whole range of fractional statistics. In the non-Abelian theory, we find a superfluid (and superconductive) phase, which is smoothly connected with the Abelian superfluid phase originally discovered by Laughlin. The characteristic massless excitation is the Goldstone particle of the specific mechanism of spontaneous symmetry breaking. An additional massive mode is found by diagonalizing the non-Abelian, non-local, Hamiltonian in the radial gauge.

Latex file, 35 pages, 2 Latex figures included

References in corpus (10)

• Self-Dual Chern-Simons Theories
• Infinite Symmetry in the Quantum Hall Effect
• Fock Representations of Quantum Fields with Generalized Statistic
• Large N Limit in the Quantum Hall Effect
• Non-Abelian Chern-Simons Particles and their Quantization
• Perturbative Analysis of Nonabelian Aharonov-Bohm Scattering
• Differential Regularization of a Non-relativistic Anyon Model
• Perturbative Renormalizations of Anyon Quantum Mechanics
• Edge Asymptotics of Planar Electron Densities
• Chern-Simons superconductivity

Cited by in corpus (5)

• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Energy-pressure relation for low-dimensional gases
• Statistical Mechanics of an Ideal Gas of Non-Abelian Anyons
• Non-Abelian Anyon Superconductivity
• The Lattice $\beta$-function of Quantum Spin Chains