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Modern Physics Letters B

GROUND-STATE ENERGY FOR 1D (t, U, X)-MODEL AT LOW DENSITIES

Florin D. Buzatu

Published Oct 30, 1992• 1 citation
Publisher

Abstract

In describing the properties of quasi-1D materials with a highly-screened interelectronic potential, an attractive hopping term has to be added to the Hubbard Hamiltonian. The effective interaction and the ground-state energy in ladder approximation are analyzed. At low electronic densities; the attractive part of the interaction, initially smaller than the repulsive term, can become more effective, the ground-state energy decreasing below the unperturbed value.

DOI
10.1142/s0217984992001307

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In describing the properties of quasi-1D materials with a highly-screened interelectronic potential, an attractive hopping term has to be added to the Hubbard Hamiltonian. The effective interaction and the ground-state energy in ladder approximation are analyzed. At low electronic densities; the attractive part of the interaction, initially smaller than the repulsive term, can become more effective, the ground-state energy decreasing below the unperturbed value.
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The ground-state instabilities for a one-dimensional lattice system of electrons with onsite (Hubbard) and bond-site (hopping) interactions are analyzed in a perturbative approach. The zero temperature phase diagram at different band fillings is drawn; an attractive (repulsive) bond-site interaction favors the appearance of a superconductor state at low concentrations of electrons (holes). A comparison with the exact results for the Hubbard model and previous works for particular cases is also discussed.
We study the ground state phase diagrams of the extended Hubbard model with the pairhopping interaction J, i.e. the PensonKolbHubbard model.We concentrate on the case of attractive J (J > 0) which can stabilise s-wave pairing superconductivity in the system and competes with the on-site repulsive U .The evolution of the phase diagrams and order parameters for arbitrary electron density and representative values of the interaction parameters are analyzed within the (broken symmetry) HartreeFock approximation.The calculations are performed for the case of nearest-neighbors electron hopping t on the d = 2 square lattice.
The ground-state energy E and momentum distribution n k of the electrons are expanded from the atomic limit for the half-filled Hubbard model. The coefficients of expansion are represented by the spin correlation functions of the spin 1 / 2 Heisenberg model. Using the spin-wave theory, approximate values of coefficients are calculated for the square lattice and the simple cubic lattice. In one dimension, the theory shows a good agreement with the exact solution. An effective spin Hamiltonian for the half-filled Hubbard model with arbitrary hopping integrals is obtained up to the fifth order. It is shown that the fourth term contains four spin interactions.
In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [Abdelwahab et al., preceding paper, Phys. Rev. B 96, 035445 (2017)]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electron-electron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely, paramagnetic Mott insulators, Luttinger liquids, and spin-1/21/21/2 Heisenberg chains. The validity of the effective ladder models is assessed for selected parameters by studying the dependence of results on the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-one-dimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate.