Solution of the infinite range t-J model

TL;DR

This paper solves the infinite range t-J model by leveraging permutation symmetry to explicitly find energy eigenvalues and eigenstates, providing insights into the model's ground states and related Hubbard model.

Contribution

It introduces an exact solution method for the infinite range t-J model using permutation group properties, which was previously unresolved.

Findings

Explicit eigenvalues and eigenstates derived

Degenerate ground states of the finite U Hubbard model identified

Permutation symmetry simplifies the diagonalization process

Abstract

The t-J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields an additive constant. Therefore the real problem is to diagonalize the "t- model", or equivalently the infinite U Hubbard Hamiltonian. Using extensively the properties of the permutation group, we are able to find explicitly both the energy eigenvalues and eigenstates, labeled according to spin quantum numbers and Young diagrams. As a corollary we also obtain the degenerate ground states of the finite $U$ Hubbard model with infinite range hopping -t>0.