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Physical review. B, Condensed matter

Exact solution of thet-Jmodel in one dimension at 2t=±J: Ground state and excitation spectrum

P.-A. Bares, G. Blatter, Masao Ogata

Published Jul 1, 1991• 182 citations
Publisher

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.

DOI
10.1103/physrevb.44.130

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arXiv:cond-mat/0009075•Journal of the Physical Society of Japan•Dec 15, 2000•2 citations
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 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​, respectively. An interpretation of the energy spectrum in terms of spinons and holons is appropriate at low energies.
Using the Bethe-Ansatz technique, we diagonalize exactly the one-dimensional t-J Hamiltonian for the supersymmetric case t=J. In this limit it is identical with models considered previously by Sutherland and by Schlottmann. The ground state is a liquid of singlet pairs of varying spatial separation for all band fillings. We find two types of gapless excitations with effective Fermi surfaces at 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​ which we identify with the holon and the spinon excitations near half filling.
Using the Bethe-Ansatz technique, we diagonalize exactly the one-dimensional t-J Hamiltonian for the supersymmetric case t=J. In this limit it is identical with models considered previously by Sutherland and by Schlottmann. The ground state is a liquid of singlet pairs of varying spatial separation for all band fillings. We find two types of gapless excitations with effective Fermi surfaces at 2kF{\mathit{k}}_{\mathit{F}}kF​ and kF{\mathit{k}}_{\mathit{F}}kF​ which we identify with the holon and the spinon excitations near half filling.
The authors considers the one-dimensional SU(N)-invariant t-J model which consists of electrons with N spin components on a lattice with nearest-neighbour hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighbouring lattice sites. The model is integrable at the supersymmetric point t=J. The ground state Bethe ansatz equations are analysed and solved numerically for arbitrary band filling and several values of N. The ground state energy, the chemical potential and the spin susceptibility are obtained as a function of band filling. The elemental charge and spin excitations are derived for arbitrary N and band filling. The energy of the charge excitations vanishes at the Fermi surface. The Fermi velocity has a maximum as a function of band filling, vanishing for the empty and full bands. The spinwave velocity is inversely proportional to the susceptibility. For exactly one electron per site the charge fluctuations are suppressed and the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.
The one-dimensional anisotropic t - J model was exactly solved using the Bethe ansatz . We first discuss the effect of anisotropy on the ground-state properties. We find a continuous phase transition induced by a magnetic field. The low-lying (spin and charge) excitation spectrum is obtained for various fillings. According to the anisotropy, the model has massive or massless modes for spin excitations. At half-filling, the model reduces to the spin- antiferromagnetic XXZ -model. We calculate the correct excitation continuum whose lowest mode is lower than that obtained by des Cloizeaux and Gaudin. Charge excitations are massless for any value of the anisotropy.
We consider a one-dimensional two-band model of electrons on a lattice with nearest-neighbor hopping t constrained by the excluded multiple occupancy of the sites, an interband splitting, \ensuremath{\Delta}, and intraband and interband exchange J between neighboring sites. This model is integrable at the supersymmetric point and reduces to the SU(4)-invariant supersymmetric t-J model with crystal field splitting. We present the exact solution via Bethe's ansatz and discuss ground-state properties and the excitation spectrum as a function of \ensuremath{\Delta}.
Quasi-particle picture in a magnetic field is pursued for dynamical spin and charge correlation functions of the one-dimensional supersymmetric t-J model with inverse-square interaction. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of relevant excited states are identified which are valid in the thermodynamic limit. The excitation contents are composed of spinons, antispinons, holons and antiholons obeying fractional statistics. Both longitudinal and transverse components of the dynamical spin structure factor are independent of the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. The dynamical charge structure factor does not depend on the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. These features indicate the strong spin-charge separation in dynamics, reflecting the high symmetry of the model.