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physica status solidi (b)

A Dynamical Theory for a Disordered Hubbard Chain far from Equilibrium. III. The High‐Field Case

E. Heiner

Published Aug 1, 1986• 2 citations
Publisher

Abstract

Abstract For the high‐field limit of a ID Hubbard chain (eF0a/u) ≫ 1 the expectation values for single and double occupancy are calculated. The equation for double occupancy does not contain a diffusion term. In contrast to the low‐field case the current density is not splitted in two terms.
DOI
10.1002/pssb.2221360233

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We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time evolution of these nonequilibrium states, by using numerical forward-propagation approaches to chains as long as 20 sites. For a class of typical states, we find excellent agreement with linear-response theory and unveil the existence of remarkably clean charge diffusion in the regime of strong particle-particle interactions. We additionally demonstrate that, in the half-filling sector, this diffusive behavior does not depend on certain details of our initial conditions, i.e., it occurs for five different realizations with random and nonrandom internal degrees of freedom, single and double occupation of the central site, and displacement of spin-up and spin-down particles.
We study the density of states for a structurally random Hubbard model with a half-filled band. Calculations are carried out with the hopping integral t(R) obtained from a hydrogenic 1S wave function and with an on-site Coulomb repulsion [Formula: see text]. The equation of motion for the retarded single-particle Green's function is treated in the Hubbard III decoupling approximation. The configurational averaging for the Green's function is simplified using the approximation of Kikuchi. Coefficients in the locator–interactor expansion are calculated analytically up to seventh order in t. Several approximants for this formal series are investigated, including Padé approximant, continued fraction approximation, and quadratic Padé approximant. The last two approximants yield densities of state in satisfactory agreement with the result of Aoki and Kamimura in the high concentration region and our results are expected to represent an improvement for intermediate densities. However, for very low densities the Hubbard III scheme will underestimate the effect of spin correlations and our previous treatment in the U = ∞ limit would be more appropriate for the lower Hubbard band.