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Spectrum and thermodynamics of the one-dimensional supersymmetric t - J model with 1/ r 2 exchange and hopping

James T. Liu, P. Coleman, D. F. Wang

Published Jul 2, 2021• 0 citations
Publisher

Abstract

We derive the spectrum and the 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 empirical determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.

DOI
10.17615/sjx5-c789

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We derive the spectrum and the 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 empirical determining the spinon degeneracies of each state, we are able to explicitly construct the free energy.
The one-dimensional SU(N)-invariant t-J model consists of electrons with N spin components on a lattice with nearest-neighbour hopping and spin exchange J. The multiple occupancy of the lattice sites is excluded. The model is integrable at the supersymmetric point, t=J. The discrete Bethe ansatz equations are analysed and the solutions are classified according to the string hypothesis. The thermodynamic Bethe ansatz equations are derived for arbitrary band filling in terms of thermodynamic energy potentials for the classes of eigenstates of the Hamiltonian. These equations are solved in limiting cases, e.g., S=1/2, the ground state and the high-temperature limit. If the charge fluctuations are suppressed the Bethe ansatz equations map onto those of the SU(N)-invariant Heisenberg chain.
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.
An asymptotic Bethe-ansatz solution is obtained for the one-dimensional t-J model with the 1/r2{\mathit{r}}^{2}r2 long-range exchange and transfer, for which the ground-state wave function was obtained exactly by Kuramoto and Yokoyama. The present approach makes it possible to study analytically the energy spectrum as well as bulk quantities. The calculated quantities reproduce the exact results known for low-temperature properties and correlation functions. This solution represents an application for the asymptotic Bethe ansatz to correlated electron systems.
An asymptotic Bethe-ansatz solution is obtained for the one-dimensional t-J model with the 1/r2{\mathit{r}}^{2}r2 long-range exchange and transfer, for which the ground-state wave function was obtained exactly by Kuramoto and Yokoyama. The present approach makes it possible to study analytically the energy spectrum as well as bulk quantities. The calculated quantities reproduce the exact results known for low-temperature properties and correlation functions. This solution represents an application for the asymptotic Bethe ansatz to correlated electron systems.
Abstract We analyze the thermodynamics and the critical behavior of the supersymmetric t - J model with long-range interactions. Using the transfer matrix formalism, we obtain a closed-form expression for the free energy per site both for a finite number of sites and in the thermodynamic limit. Our approach, which is different from the usual ones based on the asymptotic Bethe ansatz and generalized exclusion statistics, can in fact be applied to a large class of models whose spectrum is described in terms of supersymmetric Young tableaux and their associated Haldane motifs. In the simplest and most interesting case, we identify the five ground state phases of the model and derive the complete low-temperature asymptotic series of the free energy per site, the magnetization and charge densities, and their susceptibilities. We verify the model’s characteristic spin-charge separation at low temperatures, and show that it holds to all orders in the asymptotic expansion. Using the low-temperature asymptotic expansions of the free energy, we also analyze the critical behavior of the model in each of its ground state phases. While the standard phase is described by two independent conformal field theories (CFTs) with central charge c = 1 in correspondence with the spin and charge sectors, we find that the low-energy behavior of the and phases is that of a single c = 1 CFT. We show that the model exhibits an even richer behavior on the boundary between zero-temperature phases, where it can be non-critical but gapless, critical in the spin sector but not in the charge one, or critical with central charge c = 3/2.