We derive the spectrum and thermodynamics of the one-dimensional supersymmetric t-J model with long-range hopping and spin exchange using a set of maximal-spin eigenstates. This spectrum confirms the recent conjecture that the asymptotic Bethe-ansatz spectrum is exact. By empirically determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.

No abstract

No abstract

We derive the spectrum and thermodynamics of the 1D supersymmetric t-J model with long range hopping and spin exchange using a set of maximal spin eigenstates.This spectrum confirms the recent conjecture that the asymptotic Bethe-ansatz spectrum is exact. By empirically determining the spinon degeneracies of each state, we are able to explicitly construct the free energy. number: 71.30.+h, 74.65+n, 75.10.Jm Typeset Using REVTEX PACS 1The explicit construction of low dimensional models with Jastrow ground-state wavefunctions has attracted considerable recent interest [1][2][3][4][5][6]. In one dimension, Shastry and Haldane [5,6] have demonstrated that the ground-state of the 1D Heisenberg model with a 1/r 2 exchange interaction is a Gutzwiller state for the half filled infinite-U Hubbard model.Haldane has shown how the spectrum of this model can be written in terms of a generalized type of Jastrow wavefunction with excitations of novel statistics [7]. Kuramoto and Yokoyama [8] have recently extended these results to include holes, demonstrating that the corresponding 1D supersymmetric t-J model is also characterized by a Gutzwiller ground-state. Most recently, Kawakami has obtained an asymptotic Betheansatz (ABA) solution for the model, based on the observation that the ground-state wavefunction is a product of two-body functions [9]. Assuming factorizability, he derived the spectrum of the system, which was conjectured to be exact. The low-energy critical behavior of the model has been identified as a Luttinger liquid [10,11]; the spin and charge excitations are described independently by c = 1 conformal field theories.In the case of the 1/r 2 Bose gas [12], and the Shastry-Haldane 1/r 2 Heisenberg chain [7], the ABA has been shown to furnish the correct spectrum, despite the long-range nature of the interactions. A remarkable feature of these models is that excited states are obtained from the ground-state by introducing zeros into the Jastrow wavefunction, in a manner reminiscent of Laughlin's description of quasiparticles in the fractional quantum Hall effect.This motivates us to examine the 1/r 2 supersymmetric t-J model in a similar vein. Here, we show how this philosophy can be used to construct the excited state Jastrow wavefunctions of the 1/r 2 supersymmetric t-J model and indeed, the spectrum confirms Kawakami's conjecture. In addition to the spectrum, we are able to obtain the spin degeneracies of each state, permitting us to write the the free energy in closed form.The Hamiltonian for the one-dimensional t-J model is given bywhere we implicitly project out any double occupancies. We take t ij = J ij = t/d 2 (i−j) where