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arXiv:0705.3255 · Physical Review B

Spinon-holon interactions in an anisotropic t−J chain: A comprehensive study

Jurij Šmakov, A. L. Chernyshev, Steven R. White

Published Sep 10, 2007• 11 citations
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Abstract

We consider a generalization of the one-dimensional $t\text{\ensuremath{-}}J$ model with anisotropic spin-spin interactions. We show that the anisotropy leads to an effective attractive interaction between the spinon and holon excitations, resulting in a localized bound state. Detailed quantitative analytic predictions for the dependence of the binding energy on the anisotropy are presented and are verified by precise numerical simulations. The binding energy is found to interpolate smoothly between a finite value in the $t\text{\ensuremath{-}}{J}_{z}$ limit and zero in the isotropic limit, going to zero exponentially in the vicinity of the latter. We identify changes in spinon dispersion as the primary factor for this nontrivial behavior.

DOI
10.1103/physrevb.76.115106

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We consider a generalization of the one-dimensional t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model with anisotropic spin-spin interactions. We show that the anisotropy leads to an effective attractive interaction between the spinon and holon excitations, resulting in a localized bound state. Detailed quantitative analytic predictions for the dependence of the binding energy on the anisotropy are presented and are verified by precise numerical simulations. The binding energy is found to interpolate smoothly between a finite value in the t\ensuremath-Jzt\text{\ensuremath{-}}{J}_{z}t\ensuremath-Jz​ limit and zero in the isotropic limit, going to zero exponentially in the vicinity of the latter. We identify changes in spinon dispersion as the primary factor for this nontrivial behavior.
We study the binding of a holon and a spinon in the one-dimensional anisotropic t-J model using a Bethe-Salpeter equation approach, exact diagonalization, and density matrix renormalization group methods on chains of up to 128 sites. We find that holon-spinon binding changes dramatically as a function of anisotropy parameter alpha=J( perpendicular)/J(z): it evolves from an exactly deducible impuritylike result in the Ising limit to an exponentially shallow bound state near the isotropic case. A remarkable agreement between the theory and numerical results suggests that such a change is controlled by the corresponding evolution of the spinon energy spectrum.
We consider an integrable model describing an Anderson-like impurity coupled to an open ttt-JJJ chain. Both the hybridization (i.e., its coupling to bulk chain) and the local spectrum can be controlled without breaking the integrability of the model. As the hybridization is varied, holon and spinon bound states appear in the many body ground state. Based on the exact solution we study the state of the impurity and its contribution to thermodynamic quantities as a function of an applied magnetic field. Kondo behavior in the magnetic response of the impurity can be observed provided that its parameters have been adjusted properly to the energy scales of the holon and spinon excitations of the one-dimensional bulk.
We consider the effects of interactions on spinon excitations in Heisenberg spin-1/2 chains. We compute the exact two-spinon part of the longitudinal structure factor of the infinite chain in zero field for all values of anisotropy in the gapless antiferromagnetic regime, via an exact algebraic approach. Our results allow us to quantitatively describe the behavior of these fundamental excitations throughout the observable continuum, for cases ranging from free to fully coupled chains, thereby explicitly mapping the effects of "turning on the interactions" in a strongly correlated system.
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 large-scale determinant quantum Monte Carlo simulations in combination with the stochastic analytical continuation, we study two-particle dynamical correlation functions in the anisotropic square lattice of weakly coupled one-dimensional (1D) Hubbard chains at half filling and in the presence of weak frustration. The evolution of the static spin structure factor upon increasing the interchain coupling is suggestive of the transition from the power-law decay of spin-spin correlations in the 1D limit to long-range antiferromagnetic order in the quasi-1D regime and at T=0T=0T=0. In the numerically accessible regime of interchain couplings, the charge sector remains gapped. The low-energy momentum dependence of the spin excitations is well described by the linear spin-wave theory with the largest intensity located around the antiferromagnetic wave vector. This magnon mode corresponds to a bound state of two spinons. At higher energies the spinons deconfine and we observe signatures of the two-spinon continuum which progressively fade away as a function of interchain hopping.