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Physical review. B, Condensed matter

Numerical study of charge and spin separation in low-dimensional systems

E. A. Jagla, K. Hallberg, C. A. Balseiro

Published Mar 1, 1993• 42 citations
Publisher

Abstract

We study numerically the charge and spin separation in low-dimensional systems with local interactions. We consider finite Hubbard systems in one and two dimensions and calculate the ground state. An electron is added to the system in a spatially localized state. The time evolution of this state is obtained and the charge and spin densities are evaluated for different times. In one dimension the charge and spin-wave packets propagate with different velocities. The results are interpreted in terms of the Bethe-ansatz solution. In two dimensions the effect of charge and spin separation is not clearly observed, probably because of the small size of the system.

DOI
10.1103/physrevb.47.5849

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We study numerically the charge and spin separation in low-dimensional systems with local interactions. We consider finite Hubbard systems in one and two dimensions and calculate the ground state. An electron is added to the system in a spatially localized state. The time evolution of this state is obtained and the charge and spin densities are evaluated for different times. In one dimension the charge and spin-wave packets propagate with different velocities. The results are interpreted in terms of the Bethe-ansatz solution. In two dimensions the effect of charge and spin separation is not clearly observed, probably because of the small size of the system.
Using the time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsion, UUU and VVV, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit nonmonotonic dependence on VVV. For small and intermediate values of VVV, both velocities increase with VVV. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by VVV. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit and an effective model in the strong-coupling regime.
The question of spin-charge separation in two-dimensional lattices has been addressed by numerical simulations of the motion of one hole in a half-filled band. The calculations have been performed on finite clusters with Hubbard and t-J models. By comparing the time evolution of spin and charge polarization currents in one and two dimensions, evidence in favor of spin-charge separation in two dimensions is presented. In contrast with this, spin-charge separation is absent in a highly doped, metallic, system.
A system of one-dimensional electrons interacting via a short-range potential described by Hubbard model is considered in the regime of strong coupling using the Bethe ansatz approach. We study its momentum distribution function at zero temperature and find one additional singularity at the 3kF3{k}_{\mathrm{F}}3kF​ point. We identify that the second singularity is of the same Luttinger liquid type as the low-energy one at kF{k}_{\mathrm{F}}kF​. By calculating the spectral function simultaneously, we show that the second Luttinger liquid at 3kF3{k}_{\mathrm{F}}3kF​ is formed by charge modes only, unlike the known one around kF{k}_{\mathrm{F}}kF​ consisting of both spin and charge modes. This result reveals the ability of the spin-charge separation effect to split the Fermi point of free electrons into two, demonstrating its robustness beyond the low-energy limit of Luttinger liquid where it was originally found.
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 calculate the nonequilibrium dynamic evolution of a one-dimensional system of two-component fermionic atoms after a strong local quench by using a time-dependent spin-density-functional theory. The interaction quench is also considered to see its influence on the spin-charge separation. It is shown that the charge velocity is larger than the spin velocity for the system of on-site repulsive interaction (Luttinger liquid), and vise versa for the system of on-site attractive interaction (Luther-Emery liquid). We find that both the interaction quench and polarization suppress the spin-charge separation.
Using the adaptive time-dependent density-matrix renormalization group method for the 1D Hubbard model, the splitting of local perturbations into separate wave packets carrying charge and spin is observed in real time. We show the robustness of this separation beyond the low-energy Luttinger liquid theory by studying the time evolution of single particle excitations and density wave packets. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap at the boundary between liquid and Mott-insulating phases. We give quantitative estimates for an experimental observation of spin-charge separation in an array of atomic wires.