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arXiv:cond-mat/9608042 · Physical review. B, Condensed matter

Spectral flow in the supersymmetrict-Jmodel with a 1/ r2 interaction

Takahiro Fukui, Norio Kawakami

Published Aug 15, 1996• 10 citations
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Abstract

The spectral flow in the supersymmetric t-J model with 1/${\mathit{r}}^{2}$ interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although fractional exclusion statistics for the spin sector clearly shows up in the period of the spectral flow at half filling, such a property is generally hidden once any number of holes are doped because the commensurability condition in the motif is not met in the metallic phase. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.5346

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The spectral flow in the supersymmetric t-J model with 1/r2{\mathit{r}}^{2}r2 interaction is studied by analyzing the exact spectrum with twisted boundary conditions. The spectral flows for the charge and spin sectors are shown to nicely fit in with the motif picture in the asymptotic Bethe ansatz. Although fractional exclusion statistics for the spin sector clearly shows up in the period of the spectral flow at half filling, such a property is generally hidden once any number of holes are doped because the commensurability condition in the motif is not met in the metallic phase. \textcopyright{} 1996 The American Physical Society.
The exact solution of the spin chain model with 1/r21/{r}^{2}1/r2 exchange is found for twisted boundary conditions. The spectrum thus obtained can be reproduced by the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined exactly as a function of the twist angle. We find that the period $4\ensuremath{\pi}$ for the ground state nicely fits in with the notion of fractional exclusion statistics.
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.
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.
Dynamical properties, such as dynamical spin and charge structure factors and single-particle spectral functions, are studied for the one-dimensional supersymmetric t-J model with inverse-square interaction. Exact diagonalization and the recursion method are used for finite systems up to 16 sites. A simple rule is proposed to understand the supermultiplet structure in the excitation spectrum. Numerical calculations show that the dynamical spin structure factor is independent of the electron density in the region where only two spinons contribute. In the electron removal spectrum from half-filling, close correspondence is found between the dominant contribution from three-spinon plus one-holon states in the t-J model and the two-spinon excitations in the Haldane-Shastry model. Comparison is made with dynamics of the nearest-neighbor supersymmetric t-J model.
The dynamical properties of the one-dimensional supersymmetric t-J model in a magnetic field at T=0 are investigated within the framework of the one-dimensional Landau-liquid theory. The effect of the magnetic field on the low-energy excitation spectrum is analyzed. The transport properties of the t-J model are studied in the low-frequency long-wavelength regime. The effective charge and spin of the elementary carriers are evaluated from the spectral currents. A microscopic criterion for the separation of charge and spin degrees of freedom is established and it is shown that the charge-spin recombination across the ferromagnetic boundary is complete in the supersymmetric t-J model. The charge and spin stiffnesses are expressed in terms of the matrix elements of electronic charge and spin fluctuations between Bethe eigenstates.