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arXiv:cond-mat/9608025

Dynamics of the Two-Site Hubbard Model

A. T. Costa, M. T. Thomaz

Published Aug 6, 1996• 0 citations
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Abstract

The dynamical evolution of a two-site Hubbard model is derived in the presence of an uniform external magnetic field for a general initial state. The time evolution of the half-filled (two-particle) case has a complex behaviour. Under certain initial conditions, the average number of fermions in one-particle state, in the half-filled case, is not necessarily periodic, even though the magnetization remains periodic. The results obtained may be applied to study the magnetization and the transition dipole moment of the organic charge-transfer salts in the in-phase mode.

DOI
10.48550/arxiv.cond-mat/9608025

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The dynamical evolution of a two-site Hubbard model is derived in the presence of an uniform external magnetic field for a general initial state. The time evolution of the half-filled (two-particle) case has a complex behaviour. Under certain initial conditions, the average number of fermions in one-particle state, in the half-filled case, is not necessarily periodic, even though the magnetization remains periodic. The results obtained may be applied to study the magnetization and the transition dipole moment of the organic charge-transfer salts in the in-phase mode.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
We present a cluster dynamical mean-field treatment of the Hubbard model on a square lattice to study the evolution of magnetism and quasiparticle properties as the electron filling and interaction strength are varied. Our approach for solving the dynamical mean-field equations is an extension of Potthoff's ``two-site'' method [Phys. Rev. B. 64, 165114 (2001)], where the self-consistent bath is represented by a highly restricted set of states. As well as the expected antiferromagnetism close to half-filling, we observe distortions of the Fermi surface. The proximity of a van Hove point and the incipient antiferromagnetism lead to the evolution from an electronlike Fermi surface away from the Mott transition, to a holelike one near half-filling. Our results also show a gap opening anisotropically around the Fermi surface, close to the Mott transition (reminiscent of the pseudogap phenomenon seen in the cuprate high-Tc{T}_{c}Tc​ superconductors). This leaves Fermi arcs that are closed into pockets by lines with very small quasiparticle residue.
The Hubbard model is studied in which disorder is introduced by putting the on-site interaction to zero on a fraction f of (impurity) sites of a square lattice. Using Quantum Monte Carlo methods and Dynamical Mean–Field Theory we find that antiferromagnetic long–range order is initially enhanced at half–filling and stabilized off half-filling by the disorder. The Mott-Hubbard charge gap of the pure system is broken up in two pieces by the disorder: one incompressible state remains at average density n = 1 and another can be seen slightly below n = 1 + f. Qualitative explanations are provided.
The one-dimensional SU(n)(n)(n) Hubbard model is investigated using an analytical, perturbative renormalization-group treatment in the fermionic formulation of the model for n>2n>2n>2. It is found that in the half-filled case, the umklapp processes couple the spin and charge degrees of freedom and generate a finite gap for arbitrary finite positive UUU. This behavior is thus different from that at 1∕n1∕n1∕n filling, where there is one particle per site, in which case the dynamics of the two degrees of freedom can be separated and a critical Uc{U}_{\mathrm{c}}Uc​ is needed for the Mott transition.
A detailed quantitative study of the physical properties of the infinite-dimensional Hubbard model at half filling is presented. The method makes use of an exact mapping onto a single-impurity model supplemented by a self-consistency condition. This coupled problem is solved numerically. Results for thermodynamic quantities (specific heat, entropy, . . .), one-particle spectral properties, and magnetic properties (response to a uniform magnetic field) are presented and discussed. The nature of the Mott-Hubbard metal-insulator transition found in this model is investigated. A numerical solution of the mean-field equations inside the antiferromagnetic phase is also reported.
Abstract We consider the extended Hubbard model on a two-dimensional square lattice at half-filling. The model is investigated using the strong coupling diagram technique. We sum infinite series of ladder diagrams allowing for full-scale charge and spin fluctuations and the actual short-range antiferromagnetic order for nonzero temperatures. In agreement with earlier results, we find the first-order phase transition in the charge subsystem occurring at v = v c ≳ U/4 with v and U the intersite and on-site Coulomb repulsion constants. The transition reveals itself in an abrupt sign change of a sharp maximum in the zero-frequency charge susceptibility at the corner of the Brillouin. States arising at the transition have alternating deviations of electron occupations from the mean value on neighboring sites. Due to fluctuations, these alternating occupation deviations have short-range order. For the considered parameters, such behavior is found for U ≲ 5t with t the hopping constant. For the insulating case U ≳ 6t, in which the transition is not observed, we find a continuous growth of the Mott gap with v. The evolution of the electron density of states with increasing v is also considered.