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arXiv:cond-mat/0012432 · Journal of Physics A Mathematical and General

Some remarks about quantum diffusion for Hubbard models

Rémy Mosseri

Published Aug 10, 2000• 4 citations
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Abstract

Some exact results are given, that connect, for a general magnitude of the interaction term U , the repulsive and attractive Hubbard models, in terms of the eigenspectra and quantum diffusion properties. In particular, it is shown that, for some initial conditions, the quantum evolution cannot differentiate between the attractive and repulsive models. These results apply to both fermionic and bosonic models, in any dimension and for general filling, as far as the underlying structure is bi-partite.

DOI
10.1088/0305-4470/33/33/103

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Some exact results are given, that connect, for a general magnitude of the interaction term U , the repulsive and attractive Hubbard models, in terms of the eigenspectra and quantum diffusion properties. In particular, it is shown that, for some initial conditions, the quantum evolution cannot differentiate between the attractive and repulsive models. These results apply to both fermionic and bosonic models, in any dimension and for general filling, as far as the underlying structure is bi-partite.
We study the dynamics and the entanglement between two interacting identical bosons performing a quantum walk on a 1D lattice. The system is described by the Hubbard model, and the interaction among the particles can be either attractive or repulsive. We show that there are clear signatures - both in the evolution and in the correlations - that allow a distinction between the two cases, and we demonstrate that these features result to be intimately connected with the bandstructure and the eigenstates of the Hubbard Hamiltonian.
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