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arXiv:cond-mat/9806202

Exact Result on Hole Dynamics of One-Dimensional Supersymmetric t-J Model with Long Range Interaction

Yusuke S. Kato

Published Jun 17, 1998• 0 citations
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Abstract

We obtain an exact result on single hole dynamics in one-dimensional Mott-insulators through the study on the supersymmetric t-J model with long range interaction at half-filling. We calculate the expression G_{1s1h}(x,t) for one spinon one holon contribution to the hole propagator. We find that G_{1s1h}(x=0,t=0)=3/8, which amounts to 75% of the spin-fixed mean particle density 1/2.

DOI
10.48550/arxiv.cond-mat/9806202

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We obtain an exact result on single hole dynamics in one-dimensional Mott-insulators through the study on the supersymmetric t-J model with long range interaction at half-filling. We calculate the expression G_{1s1h}(x,t) for one spinon one holon contribution to the hole propagator. We find that G_{1s1h}(x=0,t=0)=3/8, which amounts to 75% of the spin-fixed mean particle density 1/2.
We obtain an exact result on the single-hole dynamics in one-dimensional Mott-Hubbard insulators through a study of the supersymmetric $t\ensuremath{-}J$ model with long-range interaction at half filling. We calculate the expression G1s1h(x,t){G}_{1s1h}(x,t)G1s1h​(x,t) for the one-spinon one-holon contribution to the hole propagator, which contributes 7575%75 of the total spectral weight. The matrix element is independent of the holon momentum. The spectral weight has an inverse square root singularity along the holon band. Comparison with the hole dynamics of the $U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\infty}$ Hubbard model is also made.
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.
By deriving and studying the coordinate representation for the one-spinon one-holon wave function we show that spinons and holons in the supersymmetric $t\ensuremath{-}J$ model with 1/r2{1/r}^{2}1/r2 interaction attract each other. The interaction causes a probability enhancement in the one-spinon one-holon wave function at short separation between the particles. We express the hole spectral function for a finite lattice in terms of the probability enhancement, given by the one-spinon one-holon wave function at zero separation. In the thermodynamic limit, the spinon-holon attraction turns into the square-root divergence in the hole spectral function.
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.
Holes in a Mott insulator are represented by spinless fermions in the fermion-boson model introduced by Edwards. Although the physically interesting regime is for low to moderate fermion density, the model has interesting properties over the whole density range. It has previously been studied at half-filling in the one-dimensional (1D) case by numerical methods, in particular using exact diagonalization and the density matrix renormalization group (DMRG). In the present study the one-particle Green's function is calculated analytically by means of a decoupling scheme for the equations of motion, valid for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero boson relaxation parameter. The Green's function is used to compute some ground state properties, and the one-fermion spectral function, for fermion densities n = 0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numerical results obtained using the DMRG and dynamical DMRG, and new light is shed on the nature of the ground state at different fillings. The Green's function approximation is sufficiently successful in 1D to justify future application to the 2D and 3D cases.