Exact Solution of a One-Dimensional Multicomponent Lattice Gas with Hyperbolic Interaction

TL;DR

This paper provides an exact solution for a one-dimensional multicomponent quantum lattice model with a variable-range hyperbolic interaction, bridging known models and enabling detailed analysis of physical properties.

Contribution

It introduces an exact solution for a new class of multicomponent lattice models with hyperbolic interactions, extending previous nearest-neighbor and inverse-square models.

Findings

Explicit formulas for energy, susceptibility, and charge stiffness.

Dispersion relations for low-lying excitations.

Dependence of properties on interaction range and fermion species.

Abstract

We present the exact solution to a one-dimensional multicomponent quantum lattice model interacting by an exchange operator which falls off as the inverse-sinh-square of the distance. This interaction contains a variable range as a parameter, and can thus interpolate between the known solutions for the nearest-neighbor chain, and the inverse-square chain. The energy, susceptibility, charge stiffness and the dispersion relations for low-lying excitations are explicitly calculated for the absolute ground state, as a function of both the range of the interaction and the number of species of fermions.