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Physical Review Letters

Spin and Charge Dynamics of the t−J Model

Takami Tohyama, Peter Horsch, Sadamichi Maekawa

Published Feb 6, 1995• 69 citations
Publisher

Abstract

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 ($n>0.7$), a remarkable feature emerges: $S(\mathrm{Q}, \ensuremath{\omega})$ shows a pronounced peak at low energy of order $J$ which is consistent with $2{k}_{F}$ low-energy excitations, whereas low-energy $2{k}_{F}$-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.

DOI
10.1103/physrevlett.74.980

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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, ${\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 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.
The density- and spin-correlation functions of the t model are calculated on a square lattice in leading order of a 1/N expansion using X operators and a Baym-Kadanoff expansion. While the spectra of both correlation functions are similar at low densities, the energy scale for density fluctuations becomes much higher than that of spin fluctuations at large densities, due to collective effects. Our results agree quite well with recent exact diagonalizations for the case N=2. Furthermore, we examine the idea that the charge correlations of strongly correlated electrons with spin can be described by those of uncorrelated spinless electrons in two dimensions. While the equal-time density correlation functions of both systems are similar, the dynamic ones behave quite differently at high densities.
The density response function $N(\mathrm{q}, \ensuremath{\omega})$ of the two-dimensional $t\ensuremath{-}J$ model is studied starting from a mixed-gauge formulation of the slave-boson approach. Our results for $N(\mathrm{q}, \ensuremath{\omega})$ are in remarkable agreement with exact diagonalization studies, and provide a natural explanation of the anomalous features in the density response in terms of the spin-polaron nature of the charge carriers. In particular, we have identified unexplained low-energy structures in the diagonalization data as arising from the coherent polaron motion of holes in a spin liquid.
We present an exact diagonalization study of the low-energy singlet and triplet states for both the one-dimensional (1D) and 2D t-J models. A scan of the parameter ratio J/t shows that for most low-energy states in both 1D and 2D the excitation energy takes the form E(t,J)=a\ensuremath{\cdot}t+b\ensuremath{\cdot}J. In 1D this is the natural consequence of the factorization of the low-energy wave functions, i.e., spin-charge separation. Examination of the low-energy eigenstates in 2D shows that most of these are collective modes, which for larger J correspond to a periodic modulation of the hole density. The modulation is well reproduced by treating holes as hard-core bosons with an attractive interaction.
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.