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Physica B Condensed Matter

Pairing of particles in a one-dimensional Fibonacci lattice within the generalized Hubbard model

José Eduardo Espinosa, A. Quiroz

Published Feb 18, 2005• 0 citations
Publisher
DOI
10.1016/j.physb.2005.01.219

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In this work we analyzed the ground-state symmetry for the cases of two particles in a linear Fibonacci chain, using the generalized Hubbard Hamiltonian and a previously developed real-space mapping method. The method is based on mapping the correlated many-body problem onto an equivalent site-and bond-impurity one-body problem in a higher dimensional space, where the problem can be solved exactly. For the case of two particles, it is obtained a ground-state when the correlated hopping interactions are included. The two particle problem is analyzed by looking at the phase diagram for the bound state. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
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Expansion dynamics of interacting fermions in a lattice is simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and nonpaired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.