1D Generalized Statistics Gas: A Gauge Theory Approach

Abstract

A field theory with generalized statistics in one space dimension is introduced. The statistics enters the scene through the coupling of the matter fields to a statistical gauge field, as it happens in the Chern-Simons theory in two dimensions. We study the particle-hole excitations and show that the long wave length physics of this model describes a gas obeying the Haldane generalized exclusion statistics. The statistical interaction is found to provide a way to describe the low-T critical properties of one-dimensional non-Fermi liquids.

Anyons and Chiral Solitons on a Line

“…Finally we show that the model of Ref. [1], though failing to achieve its announced goal, possesses an interesting and novel soliton structure.…”

“…Recently there has appeared in these pages an article offering a similar description for particles on a line [1]. However, the claimed results are incorrect; apparently inattention to signs has led to error.…”

“…[1]. We present an alternative nonrelativistic field theory, which succeeds in describing lineal anyons, but is not a gauge theory.…”

Simulating an Interacting Gauge Theory with Ultracold Bose Gases

“…A more modest problem that generated intense interest in the late 1990s was the quest for finding a pure gauge theory with solutions given by the one-dimensional analog of the well-known twodimensional anyons [11]. The first attempt in this direction [12] failed to describe one-dimensional anyon solutions [13], but the associated semiclassical, nonlinear model of the interacting gauge theory supported chiral solitons, as shown by Aglietti, Griguolo, Jackiw, Pi, and Seminara (AGJPS) in Ref. [14].…”

Clusters of bound particles in the derivative δ-function Bose gas

“…The Hamiltonian (1.2) of this derivative δ-function Bose gas can be obtained by projecting that of an integrable derivative nonlinear Schrödinger (DNLS) quantum field model on the N-particle subspace. Classical and quantum versions of such DNLS field models have found applications in different areas of physics like circularly polarized nonlinear Alfven waves in plasma, quantum properties of optical solitons in fibers, and in some chiral Tomonaga-Luttinger liquids obtained from the Chern-Simons model defined in two dimensions [34][35][36][37][38][39][40][41]. The scattering and bound states of the derivative δ-function Bose gas (1.2) have been studied extensively by using the methods of coordinate as well as algebraic Bethe ansatz [29][30][31][32][33][42][43][44].…”