Quantum Monte Carlo study of confined fermions in one-dimensional optical lattices
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Using quantum Monte Carlo (QMC) simulations we study the ground-state properties of the one-dimensional fermionic Hubbard model in traps with an underlying lattice. Since due to the confining potential the density is space dependent, Mott-insulating domains always coexist with metallic regions, such that global quantities are not appropriate to describe the system. We define a local compressibility that characterizes the Mott-insulating regions and analyze other local quantities. It is shown that the momentum distribution function, a quantity that is commonly considered in experiments, fails in giving a clear signal of the Mott-insulator transition. Furthermore, we analyze a mean-field approach to these systems and compare it with the numerically exact QMC results. Finally, we determine a generic form for the phase diagram that allows us to predict the phases to be observed in the experiments.
RevTex file, 13 pages, 19 figures, published version
RevTex file, 13 pages, 19 figures, published version