Simple parameterization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity

Abstract

Simple analytical parameterizations for the ground-state energy of the one-dimensional repulsive Hubbard model are developed. The charge dependence of energy is parameterized using exact results extracted from the Bethe-ansatz (BA). The resulting parameterization is shown to be in better agreement with highly precise data obtained from a fully numerical solution to the BA equations than previous expressions (Lima et al 2003 Phys. Rev. Lett. 90 146402). Unlike these earlier proposals, the present parameterization correctly predicts a positive Mott gap at half filling for any U > 0. The construction is extended to spin-dependent phenomena by parameterizing the magnetization dependence of the ground-state energy using further exact results and numerical benchmarking. Lastly, the parameterizations developed for the spatially uniform model are extended by means of a simple local-density-type approximation to spatially inhomogeneous models, e.g. in the presence of impurities, external 2 fields or trapping potentials. The results are shown to be in excellent agreement with independent many-body calculations, at a fraction of the computational cost.

Interacting fermions in one-dimensional disordered lattices: Exploring localization and transport properties with lattice density-functional theories

“…[30][31][32][33][34][35][36][37][38][39] On the other hand, the use of lattice TDDFT to describe the nonequilibrium dynamics of Hubbard-like models is a rather new topic [40][41][42][43] ; firm conceptual ground was initially established for approaches based on lattice bond currents, [44][45][46] …”

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

“…This deficiency is corrected in our second level parametrization p2TBA of Eq. (30). As a result the density calculated with the p2TBA Hxc potential is completely indistinguishable from that obtained using the full numerical TBA potential.…”

“…(30)) in the zero-temperature limit with the parametrization of Ref. 30 (which in the following is denoted as FVC) and exact zero-temperature results reveals that the p2TBA parametrization in some density ranges can be marginally less accurate than FVC. As pointed out before, however, in contrast to FVC our parametrization by construction incorporates the exact zero-temperature gap.…”

“…Hence in practice in all figures the results denoted as TBA have been actually produced using the p2TBA potential defined after Eq. (30). At strictly zero temperature, the KS potential has a real discontinuity at integer filling n = 1 and, therefore, it is undefined in this point.…”

Solving lattice density functionals close to the Mott regime

“…[37]) among which LDFT has become particularly useful. 21,38,39 Static and time-dependent [14][15][16] lattice DFT were indeed used to investigate the physics of Hubbard models with on-site interaction 13,[17][18][19][20][21][22] , Kondo models [23][24][25][26][27][28] , disordered interacting lattice models 31,32 and spin liquids 33 .…”