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arXiv:cond-mat/9309031 · Physical Review Letters

Indications of spin-charge separation in the two-dimensionalt-Jmodel

W. O. Putikka, Rodney L. Glenister, Rajiv R. P. Singh, Hirokazu Tsunetsugu

Published Jul 4, 1994• 55 citations
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Abstract

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 2${\mathbf{k}}_{\mathit{F}}^{\mathrm{SF}}$ as a characteristic wave vector. Previous studies have shown that ${\mathit{n}}_{\mathbf{k}}$ has a steplike feature at ${\mathbf{k}}_{\mathit{F}}$ and S(q) has 2${\mathbf{k}}_{\mathit{F}}$ as a characteristic wave vector. Here ${\mathit{k}}_{\mathit{F}}$ and ${\mathit{k}}_{\mathit{F}}^{\mathrm{SF}}$ 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.

DOI
10.1103/physrevlett.73.170

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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.
Using high temperature series we calculate temperature derivatives of the spin-spin and density-density correlation functions to investigate the low energy spin and charge excitations of the two-dimensional t-J model. We find that the temperature derivatives indicate different momentum dependences for the low energy spin and charge excitations. By comparing short distance density-density correlation functions with those of spinless fermions and hard core bosons, we find that the t-J model results are intermediate between the two cases, being closer to those of hard core bosons. The implications of these results for superconductivity are discussed.
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 equal-time pairing correlation function of the two-dimensional t-J model on a square lattice is studied using a high-temperature expansion method. The sum of the pairing correlation, its spatial dependence, and the correlation length are obtained as functions of temperature down to T≃0.2tT \simeq 0.2 tT≃0.2t. By comparison of single-particle contributions in the correlation functions, we find an effective attractive interaction between quasi-particles in dx2−y2d_{x^2-y^2}dx2−y2​-wave pairings. It is shown that d-wave correlation grows rapidly at low temperatures for 0.5 < n < 0.9, with n being the electron density. The temperature for this growth is roughly scaled by J/2. This is in sharp contrast to the Hubbard model in a weak or intermediate coupling region, where there is no numerical evidence of superconductivity.
We investigate the charge density correlation function in the slave fermion representation of the two-dimensional t - J model using the self-consistent perturbation approach developed for that model by Li et al (1992 Phys. Rev. B 45 5428), which to lowest order in (t, J) gives a diagrammatic equivalent to the usual mean field theory. At the lowest order the equal-time correlation function (interpreted as the holon density correlation function) shows similar features to the results of recent high-temperature series calculations. However the loop corrections, representing scattering of holes by the antiferromagnetic spin fluctuations, lead to a divergent compressibility at low temperatures for low hole dopings and small J/t, which we interpret as indicating a tendency towards phase separation at a temperature .