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Physical review. B, Condensed matter

Spin and charge dynamics for the one-dimensionalt-Jmodel

J. J. Deisz, K.-H. Luk, Mark Jarrell, D. L. Cox

Published Aug 1, 1992• 9 citations
Publisher

Abstract

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=2${\mathit{k}}_{\mathit{F}}$ 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.

DOI
10.1103/physrevb.46.3410

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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 (\ensuremathρ0{\mathrm{\ensuremath{\rho}}}_{0}\ensuremathρ0​=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.
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.
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.
We investigate the dynamical properties of the one-dimensional Hubbard model using the quantum Monte Carlo method and the numerical analytic continuation method based on the maximum entropy principle. Results for the spin, charge and current excitation spectrum are presented for various values of the coupling and the band filling for the system of 24 sites with the periodic boundary condition. We find that the total spectral density of the spin excitation exhibits a gapless structure irrespective of the coupling or the band filling. The charge excitation spectrum, on the other hand, clearly shows the gap formation at the half filled band and shifts its weight toward the higher energy region with increase of the coupling. This charge excitation gap, however, disappears with the hole doping. We also discuss the momentum dependence of the spectral functions.
We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ related to \ensuremath{\nu}, ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.
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.