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Chinese Physics Letters

Fermionic Concurrence in the Extended Hubbard Model

邓蜀萨, 顾世建

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

We study the fermionic concurrence in an extended Hubbard model. Its behaviour at the ground state and at finite temperatures for general U and V is obtained numerically and analytically for a dimer system. We also investigate the properties of the concurrence under a nonuniform field, and we find that it can be used to modulate and to increase the concurrence.

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We study the fermionic concurrence in an extended Hubbard model. Its behaviour at the ground state and at finite temperatures for general U and V is obtained numerically and analytically for a dimer system. We also investigate the properties of the concurrence under a nonuniform field, and we find that it can be used to modulate and to increase the concurrence.
A recently proposed ground-state renormalisation-group approach to the Hubbard model is generalised to finite temperatures. This new method provides a global and consistent description of the thermodynamics of the model at all temperatures. Application to the Hubbard chain with a half-filled band gives values for various thermodynamic functions which compare remarkably well with existing exact or numerical data, over all temperature ranges. The difficulties posed by Fermi-Dirac statistics in the set-up of the transformation are discussed to some extent and it is shown that these do not prevent one, at least in principle, from extending the approach to higher dimensions.
[[abstract]]The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0 < q < pi) into the state with strong antiferromagnetic correlations (q = pi) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.
The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physics in the ground state. The methods used included: the mean field approximation (BCS-Stoner type) and the estimation of the phase coherence temperature within the Kosterlitz-Thouless (KT) scenario in two dimensions. The BCS-BEC crossover was also analyzed in three dimensions, at finite temperatures, within the spin polarized Attractive Hubbard Model (AHM), going beyond the mean field approximation. In this case, the critical temperatures of the superconducting transition were determined within the self-consistent T-matrix method. The strong coupling expansion was applied to map the spin polarized AHM onto the model of hard-core bosons on the lattice.