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arXiv:cond-mat/9404045 · Physical review. B, Condensed matter

Spin-charge separation at small length scales in the two-dimensionalt-Jmodel

Claudius Gros, Roser Valentí

Published Oct 15, 1994• 4 citations
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Abstract

We consider projected wave functions for the two-dimensional t-J model. For various wave functions, including correlated Fermi-liquid and Luttinger-type wave functions, we present the static charge-charge and spin-spin structure factors. Comparisons with recent results from a high-temperature expansion by Putikka et al. indicates spin-charge separation at small length scales.

DOI
10.1103/physrevb.50.11313

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We consider projected wave functions for the two-dimensional t-J model. For various wave functions, including correlated Fermi-liquid and Luttinger-type wave functions, we present the static charge-charge and spin-spin structure factors. Comparisons with recent results from a high-temperature expansion by Putikka et al. indicates spin-charge separation at small length scales.
We have calculated the high temperature expansion for the density correlation function N(q) of the two-dimensional t-J model. On extrapolation by Pad\'e approximants to low temperatures we find that N(q) has 2kFSF{\mathbf{k}}_{\mathit{F}}^{\mathrm{SF}}kFSF​ as a characteristic wave vector. Previous studies have shown that nk{\mathit{n}}_{\mathbf{k}}nk​ has a steplike feature at kF{\mathbf{k}}_{\mathit{F}}kF​ and S(q) has 2kF{\mathbf{k}}_{\mathit{F}}kF​ as a characteristic wave vector. Here kF{\mathit{k}}_{\mathit{F}}kF​ and kFSF{\mathit{k}}_{\mathit{F}}^{\mathrm{SF}}kFSF​ are the Fermi wave vectors of the nearest-neighbor square lattice tight-binding and spinless fermion models, respectively. By comparison to known results for one dimension this suggests spin-charge separation in the two-dimensional t-J model.
We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of the t-J model, focusing on the regime of intermediate and low electron densities, ${\mathrm{\ensuremath{\rho}}}_{\mathit{e}}$0.5. In two dimensions (2D) both correlation functions agree remarkably well with the convolution of the single-particle spectral function, i.e., the simplest estimate possible within a Fermi-liquid picture. Deviations from the convolution are shown to originate from symmetry-related selection rules, which are unaccounted for in the convolution estimate. For all fillngs under consideration, we show that the low-energy peaks originate from particle-hole excitations between the Fermi momenta, as expected for a Fermi liquid. We contrast this with the behavior in 1D, where spin and density correlation function show the differences characteristic of spin-charge separation and where neither correlation function is approximated well by the convolution.
The spin- and density-correlation functions of the two-dimensional Hubbard model at low electronic density 〈n〉 are calculated in the ground state by using the power method, and at finite temperatures by using the quantum Monte Carlo technique. Both approaches produce similar results, which are in close agreement with numerical and high-temperature-expansion results for the two-dimensional t-J model. Using perturbative approximations, we show that the examination of the density-correlation function alone is not enough to support recent claims in the literature that suggested spin and charge separation in the low electronic density regime of the t-J model.
The physics of the one-dimensional t-J model may be determined at J/t\ensuremath{\rightarrow}0 (i.e., the U/t\ensuremath{\rightarrow}\ensuremath{\infty} limit of the repulsive Hubbard model) and at J/t=2 with the use of the Bethe ansatz. To get a full understanding of the charge and spin correlation functions for all values of J/t, one has to resort to numerical methods. We have used two numerical methods (the world-line quantum Monte Carlo algorithm and the quantum transfer-matrix algorithm) to get information on charge and spin static structure factors, pairing correlations, and critical exponents. The (1+1)-dimensional classical system corresponding to the one-dimensional t-J model, on which the Monte Carlo technique is used, is identified to a fifteen-vertex model. We show that the t-J model undergoes phase separation at large values of J/t. Before phase separation, both critical exponents and pairing correlations in the extended s-wave channel favor the onset of superconductivity. For low values of J/t, the model shows a U/t\ensuremath{\rightarrow}\ensuremath{\infty} Hubbard-like character.
The single-particle spectral functions for the two-dimensional t - J model are investigated in connection with spin and charge dynamics, using the exact diagonalization technique. At low electron density, Fermi liquid behavior is observed. Near half-filling, the spectral functions reveal a two-peak structure which is due to the different dynamics of spin and charge degrees of freedom. This density dependence of the spectral functions indicates a crossover from Fermi liquid behavior at low density to anomalous behavior near the Mott transition where the approximate decoupling of spin and charge excitations occurs.
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