Exact Solution of the Sutherland Model with arbitrary symmetry

TL;DR

This paper provides an exact solution for the Sutherland model with arbitrary internal symmetry, deriving all energy levels and ground state wave functions, and applies the theory to lattice versions and supersymmetric models.

Contribution

It introduces an elementary method to solve the Sutherland model with arbitrary symmetry, including supersymmetry, and characterizes the ground state explicitly.

Findings

Derived all energy levels and ground state wave function for the model.

Proved Gutzwiller wave function as ground state of supersymmetric t-J model.

Extended solutions to lattice versions of the model.

Abstract

An elementary theory is presented for solving the Sutherland model with arbitrary internal symmetry such as SU($\nu$) or a supersymmetry SU($\nu, \mu$). The ground state wave function and all the energy levels are derived. One starts with solving a variant of the model with distinguishable particles, and then (anti)symmetrizes the solution. The theory is also applied to various lattice versions of the model. It is proved that the Gutzwiller-type wave function is not only an eigenstate of the supersymmetric \it t-J \rm model, but is indeed the ground state.