Critical Properties of Quantum Many-Body Systems with 1/r^2 Interaction

TL;DR

This paper reviews recent findings on one-dimensional quantum models with 1/r^2 long-range interactions, analyzing their critical properties using advanced theoretical methods and exploring new related models.

Contribution

It provides a comprehensive review of the critical properties of various 1/r^2 quantum models and introduces a new method for analyzing models with harmonic confinement.

Findings

Critical properties characterized for multiple 1/r^2 models

Introduction of a renormalized-harmonic oscillator method

Connections to fractional quantum Hall effect models

Abstract

We review recent results obtained for a class of one-dimensional quantum models with $1/r^2$ long-range interaction. Based on the asymptotic Bethe-ansatz solution and conformal field theory, we study critical properties of the continuum boson model, the SU($\nu$) spin chain, the OSp($\nu$,1) supersymmetric {\it t-J} model, and a new hierarchy of models related to the fractional quantum Hall effect. We further investigate the class of $1/r^2$ models with harmonic confinement by means of a newly proposed method of the renormalized-harmonic oscillator solution.