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arXiv:cond-mat/0009075 · Journal of the Physical Society of Japan

Dynamical Properties of the 1/r2-Type Supersymmetrict-JModel in a Magnetic Field: Manifestation of Spin-Charge Separation

Yasuhiro Saiga, Yoshio Kuramoto

Published Dec 15, 2000• 2 citations
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Abstract

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.

DOI
10.1143/jpsj.69.3917

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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 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.
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 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.
Thermodynamics is derived rigorously for the 1D supersymmetric {\it t-J} model and its SU(K,1K,1K,1) generalization with inverse-square exchange. The system at low temperature is described in terms of spinons, antispinons, holons and antiholons obeying fractional statistics. They are all free and make the spin susceptibility independent of electron density, and the charge susceptibility independent of magnetization. Thermal spin excitations responsible for the entropy of the SU(K,1K,1K,1) model are ascribed to free para-fermions of order K−1K-1K−1.
Following the Bethe ansatz we determine the dynamical spectra of the one-dimensional supersymmetric t-J model. A series of fractionalized excitations are identified through two sets of Bethe numbers. Typical patterns in each set are found to yield wavefunctions containing elementary spin and charge carriers, manifested as distinct boundaries of the collective excitations in the spectra of single electron Green functions. In spin channels, gapless excitations fractionalized into two spin and a pair of postive and negative charge carriers, extending to finite energy as multiple continua. These patterns connect to the half-filling limit where only fractionalized spinons survive. In particle density channel, apart from spin-charge fractionalization, excitations involving only charge fluctuations are observed. Furthermore, nontrivial Bethe strings encoding bound state structure appear in channels of reducing or conserving magnetization, where spin and charge constituents can also be identified. These string states contribute significantly even to the low-energy sector in the limit of vanishing magnetization.
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.