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Journal of the Physical Society of Japan

Spin Dynamics in the Supersymmetrict–JModel with Inverse-Square Interaction

Mitsuhiro Arikawa, Takashi Yamamoto, Yasuhiro Saiga, Yoshio Kuramoto

Published Apr 15, 2004• 7 citations
Publisher

Abstract

Author: Arikawa, M. et al.; Genre: Journal Article; Issued: 2004-04; Keywords: spin dynamics; t-J model; supersymmetry; fractional statistics; Sutherland model; Title: Spin dynamics in the supersymmetric t-J model with inverse-square interaction
DOI
10.1143/jpsj.73.808

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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.
Excitation spectra in the SU(ν+1ν+1ν+1,1) supersymmetric t-J model with long-range exchange and transfer has quadratic dependence on spin and charge currents for all energies. After brief review on the supersymmetry, this paper gives a simple explanation for the spin-charge separation on the basis of a first-quantized representation. A useful identity is derived on permutation properties of SU(ννν) Jastrow-type wave functions, which constitute the ground states for a class of 1/r2r^2r2 interaction models.
The dynamical spin structure factor S zz ( Q , ω) in the small momentum region is derived analytically for the one-dimensional supersymmetric t – J model with 1/ r 2 interaction. Strong spin–charge separation is found in the spin dynamics. The structure factor S zz ( Q , ω) with a given spin polarization does not depend on electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S zz ( Q , ω). These results are derived via solution of the SU (2,1) Sutherland model in the strong coupling limit.
Dynamical charge structure factor N(Q,ω)N(Q,ω)N(Q,ω) with QQQ smaller than the Fermi wave number is derived analytically for the one-dimensional supersymmetric t-J model with 1/r21/r^21/r2 interaction. Strong spin-charge separation in dynamics is found. N(Q,ω)N(Q,ω)N(Q,ω) with given electron density does not depend on the spin polarization for arbitrary size of the system. In the thermodynamic limit, only two holons and one antiholon contribute to N(Q,ω)N(Q,ω)N(Q,ω). These results together with generalized ones for the SU(KKK,1) supersymmetric t-J model are derived via solution of the Sutherland model in the strong coupling limit.