Exact solution of the<i>t</i>-<i>J</i>model in one dimension at 2<i>t</i>=±<i>J</i>: Ground state and excitation spectrum

Abstract

The one dimensional t-J Hamiltonian is diagonalized exactly for the supersymmetric case 2t=\ifmmode\pm\else\textpm\fi{}J using the Bethe ansatz. In this limit it is identical with models previously considered by Lai, Sutherland, and Schlottmann. In the present paper we discuss the ground-state properties and excitation spectrum in zero magnetic field. The ground state is a liquid of singlet bonds with varying spatial separation. Its most remarkable feature is the presence of bonds connecting particles at arbitrarily large distances. The ground-state energy is an analytic function of the band filling. There is no difference in the chemical potential for adding one or two particles and no evidence for the binding of holes. The low-lying part of the spectrum consists of two types of gapless excitations (charge and spin) with effective Fermi surfaces at 2${\mathit{k}}_{\mathit{F}}$ and ${\mathit{k}}_{\mathit{F}}$, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.