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arXiv:cond-mat/9409102 · Physical review. B, Condensed matter

Spin and charge dynamics of the two-dimensionalt-Jmodel at intermediate electron densities: Absence of spin-charge separation

R. Eder, Y. Ohta

Published May 1, 1995• 8 citations
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Abstract

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.

DOI
10.1103/physrevb.51.11683

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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, \ensuremathρe{\mathrm{\ensuremath{\rho}}}_{\mathit{e}}\ensuremathρe​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 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.
We investigate the dynamical spin and charge correlation functions, $S(\mathrm{Q}, \ensuremath{\omega})$ and $N(\mathrm{Q}, \ensuremath{\omega})$, for the two-dimensional (2D) $t\ensuremath{-}J$ model by using the exact diagonalization technique. Both quantities are compared with the 1D $t\ensuremath{-}J$ model. At high electron density (n>0.7n>0.7n>0.7), a remarkable feature emerges: $S(\mathrm{Q}, \ensuremath{\omega})$ shows a pronounced peak at low energy of order JJJ which is consistent with 2kF2{k}_{F}2kF​ low-energy excitations, whereas low-energy 2kF2{k}_{F}2kF​-backscattering processes are strongly suppressed in the charge-density response. $N(\mathrm{Q}, \ensuremath{\omega})$ consists of a dense and broad continuum, qualitatively different from the 1D charge response, implying strong interactions between charge and spin degrees of freedom.
The dynamic spin and charge correlation functions are computed for the one-dimensional t-J model with use of world-line quantum Monte Carlo and the maximum-entropy method. By comparing our results with exactly known limits, we are able to discern the power and limitations of this method. The spin excitation spectrum shows gapless spin excitations for q=2kF{\mathit{k}}_{\mathit{F}}kF​ when J\ensuremath{\le}2t and for q=\ensuremath{\pi} when J>3.25t where phase separation occurs. Also, intermediate values of J/t show no spin gap for the large electron filling (${\mathrm{\ensuremath{\rho}}}_{0}$=0.75) considered here. For J\ensuremath{\le}2t, the charge correlations are dominated at high frequencies by excitations which are related to the particle-hole excitations found for J=0, but a low-frequency mode appears at finite values of J, which is likely related to the binding of electron pairs.
We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D $t\ensuremath{-}J$ model for hole dopings $\ensuremath{\le}25$%. Both correlation functions show a remarkably regular, but very different, scaling with both hole density ${\ensuremath{\rho}}_{h}$ and parameters ttt and JJJ. The density correlation function is most consistent with that of condensed bosons in a band of width $\ensuremath{\sim}t$, the spin correlation function with that of fermions in a band of width $\ensuremath{\sim}J$. We show that the familiar spin bag scenario explains these results in a natural way.
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 show that there are qualitative differences between the temperature dependence of the spin and charge correlations in the normal state of the 2D attractive Hubbard model using quantum Monte Carlo simulations. The one-particle density of states shows a pseudogap above Tc{T}_{c}Tc​ with a depleted N(0)N\left(0\right)N(0) with decreasing TTT. The susceptibility ${\ensuremath{\chi}}_{s}$ and the low frequency spin spectral weight track N(0)N\left(0\right)N(0), which explains the spin-gap scaling: ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}_{s}\left(T\right)$. However, collective excitations contribute to the charge channel, and the compressibility $dn/d\ensuremath{\mu}$ is TTT independent. This anomalous ``spin-charge separation'' is shown to exist even at intermediate ∣U∣|U|∣U∣ where the momentum distribution n(k)n\left(\mathbf{k}\right)n(k) gives evidence for a degenerate Fermi system.