Effects of nanoscale spatial inhomogeneity in strongly correlated systems

Abstract

We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential v i can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction U i . Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for a reexamination of model calculations assuming spatial homogeneity. A large part of the complexity of strongly correlated systems arises from the multiple phases that coexist or compete in their phase diagrams. Metallic and insulating phases are separated by metal-insulator transitions, and subject to the formation of various types of long-range order, such as antiferromagnetism, superconductivity, and charge-or spindensity waves. The relative stability of such phases is determined by differences in appropriate thermodynamic potentials, or, at zero temperature, in their ground-state energies. Identification of the appropriate order parameters and calculation of the ground-state energies of the various phases is a complicated problem, and the nature of the phase diagram of many strongly correlated systems is still subject to considerable controversy. It is widely believed, however, that a minimal model containing the essence of strong correlations, and displaying many of the above-mentioned phases, is the homogeneous Hubbard model, which in one dimension and standard notation readsMuch theoretical effort is thus going into the analysis of the homogeneous Hubbard model and the clarification of the nature of its ground state. In a parallel development, nanoscale spatial inhomogeneity has been observed experimentally to be a ubiquitious feature of strongly correlated systems, 1-8 but although its importance is widely recognized, the consequences of such inhomogeneity are still insufficiently understood. The present paper investigates the effects of, and the competition between, two different manifestations of nanoscale inhomogeneity in strongly correlated systems, namely local variations in the on-site potential and in the on-site interaction. We base our analysis on the inhomogeneous Hubbard model

Time-dependent bond-current functional theory for lattice Hamiltonians: Fundamental theorem and application to electron transport

“…In Ref. 33 the BALDA functional has already been used successfully for site-dependent interactions. It should be noted that this is a deviation from the usual LDA philosophy where the XC energy of the uniform gas is used for a non-uniform system but the interaction is unchanged.…”

“…The crucial difference is that the underlying model is the uniform Hubbard model whose exact solution can be constructed via the Bethe ansatz. Just as the XC energy of the uniform electron gas serves as input for the usual LDA, the exact XC energy per site of the uniform Hubbard model then serves as input for the Bethe-ansatz LDA (BALDA) used for non-uniform Hubbard models [32,33]. In the context of TDDFT, an adiabatic version of this functional (adiabatic BALDA, ABALDA) local in both space and time, e.g., v xc [n](i, t) = v xc (n i (t)), has been suggested by Verdozzi [10].…”

Lattice density functional theory at finite temperature with strongly density-dependent exchange-correlation potentials

“…The functional dependence of v mod Hxc (n) on the density is extracted from some interacting model system for which the exact solution can be constructed by analytical and/or numerical techniques. Probably the most prominent example of such a functional for lattice-DFT is the local density approximation (LDA) based on Betheansatz solution of the uniform Hubbard model in 1D (Bethe-ansatz LDA, BALDA) at zero temperature 4,9,24 .…”

“…The BALDA has been successfully applied to spatially inhomogeneous Hubbard supperlattices 9 , to cold fermionic atoms in a harmonic trap, both with repulsive 5 and attractive 14 electronic interaction and to the study of the static and dynamic linear density response 15,16 . Extensions of the BALDA have been suggested to systems in static magnetic fields 17 and, in the adiabatic form, to the domain of time-dependent DFT 18 where it has been used to study the dynamics of finite Hubbard clusters.…”

“…As with usual DFT, the applicability and success of lattice DFT hinges on the availability of approximations to the unknown exchange-correlation (xc) functional. Capelle and coworkers proposed a local functional for the xc energy per site based on the Betheansatz solution of the uniform 1D Hubbard model at zero temperature 4,9 . Thus, for one-dimensional lattice models, the 1D Hubbard model takes the role of the uniform electron gas in continuum formulation of DFT as an exactly solvable model system which provides the essential input for the construction of the local approximation.…”