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arXiv:cond-mat/0105523 · Physical Review Letters

Spinon-Holon Attraction in the Supersymmetric t−J Model with 1/r2 Interaction

Bogdan Andrei Bernevig, Domenico Giuliano, R. B. Laughlin

Published Oct 9, 2001• 15 citations
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Abstract

We derive the coordinate representation of the one-spinon one-holon wave function for the supersymmetric t-J model with 1/r(2) interaction. This result allows us to show that a spinon and a holon attract each other at short distance. The attraction gets stronger as the size of the system is increased and, in the thermodynamic limit, it is responsible for the square-root singularity in the hole spectral function [Y. Kato, Phys. Rev. Lett. 81, 5402 (1998)].

DOI
10.1103/physrevlett.87.177206

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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.
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.
By deriving and studying the coordinate representation for the two-spinon wave function, we show that spinon excitations in the Haldane-Shastry model interact. The interaction is given by a short-range attraction and causes an enhancement in the two-spinon wave function at short separations between the spinons. We express the spin susceptibility for a finite lattice in terms of the enhancement, given by the two-spinon wave function at zero separation. In the thermodynamic limit, the spinon attraction turns into the square-root divergence in the dynamical spin susceptibility.
The electron addition spectrum A+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A+(k,omega) has a simple analytic form with contributions from one spinon, one holon, and one antiholon-all of which obey fractional statistics. The upper edge of A+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.
The elementary excitations of strongly correlated one-dimensional electronic systems - spinons and holons - are discussed in an exact solution of the Haldane-Shastry and Kuramoto-Yokoyama model. We derive and exactly solve the equation of motion both for the two-spinon wavefunction and for the one-spinon, one-holon wavefunction. By solving the equations of motion we find the spinon-spinon and spinon-holon interaction to be a short-range attraction. The physical consequences of such an attraction on the spin-form factor and on the hole-spectral function are also worked out.