On Models with Inverse-Square Exchange

TL;DR

This paper introduces a one-dimensional quantum N-body model with inverse-square exchange interactions for fermions or bosons with SU(n) symmetry, constructing eigenstates and analyzing low-energy excitations using harmonic fluid theory.

Contribution

It constructs explicit eigenstates for both continuum and lattice models and derives harmonic fluid parameters, including velocities and correlation exponents, for the first time in this context.

Findings

Eigenstates constructed for continuum and lattice models

Derived harmonic fluid parameters like velocities and exponents

Confirmed harmonic relations among charge and spin velocities

Abstract

A one-dimensional quantum N-body system of either fermions or bosons with $SU(n)$ colors interacting via inverse-square exchange is presented in this article. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product type wave function. The class of states we construct in this paper corresponds to the ground state and the low energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state we find the harmonic fluid parameters (i.e. the charge, spin velocities, etc.), explicitly. The correlation exponent and the compressibility of are also found. As expected the general harmonic relation(i.e. $v_S=(v_Nv_J)^{1/2}$) is satisfied among the charge and spin velocities.