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Physica B Condensed Matter

Two-scale analysis of the Hubbard model

Adolfo Avella

Published Feb 28, 2003• 2 citations
Publisher
DOI
10.1016/s0921-4526(02)02630-3

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A numerical scaling analysis is used to show that Nagaoka's ferromagnetic state in the two-dimensional Hubbard model with one hole is superseded by an antiferromagnetic (AF) state with a discontinuous jump in the total spin due to the AF coupling as the Hubbard U is made finite. The same applies to the two-hole system, which has a spiral spin structure. We can show, via the scaling, that the crossover to an AF state is a precursor of a pathological coalescence of states having the minimum spin and Nagaoka's state at U=\ensuremath{\infty} in the thermodynamic limit.
The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field are theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric Hubbard model shows that a high-frequency bichromatic external field can sustain a low-energy particle bound state (a doublon) in which two fermions of different species occupy nearest-neighbor sites and cotunnel along the lattice. The predictions of the asymptotic analysis are confirmed by direct numerical simulations of the two-particle Hubbard Hamiltonian.