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Bulletin of the American Physical Society

Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice

Tiago Mendes Santos, Thereza Paiva, Raimundo R. dos Santos

Published Mar 2, 2015• 0 citations
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Abstract

We investigate the harmonic-trap control of size and shape of Mott regions in the Fermi Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50-80 samples, drastically reduce finite-size effects in some ground state properties; calculations in the grand canonical ensemble together with a local-density approximation (LDA) allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state, to a Mott core, and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A ‘phase diagram’ in terms of an effective density and the on-site repulsion is proposed, as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative) display detectable signatures of the core-ring transition. Some spin correlation functions are also calculated, and predict the existence Neel ordering within Mott cores and rings.

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Size and shape of Mott regions for fermionic atoms in a two-dimensional optical lattice

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We investigate the harmonic-trap control of the size and shape of Mott regions in the Fermi-Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50--80 samples, drastically reduces finite-size effects in some ground-state properties; calculations in the grand-canonical ensemble together with a local-density approximation allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state to a Mott core and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A ``phase diagram'' in terms of an effective density and of the on-site repulsion is proposed as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative), display detectable signatures of the core-ring transition. Some spin-correlation functions are also calculated and predict the existence N\'eel-like ordering within Mott cores and rings.

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We investigate the harmonic-trap control of size and shape of Mott regions in the Fermi Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50-80 samples, drastically reduce finite-size effects in some ground state properties; calculations in the grand canonical ensemble together with a local-density approximation (LDA) allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state, to a Mott core, and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A ‘phase diagram’ in terms of an effective density and the on-site repulsion is proposed, as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative) display detectable signatures of the core-ring transition. Some spin correlation functions are also calculated, and predict the existence Neel ordering within Mott cores and rings.
We investigate the harmonic-trap control of the size and shape of Mott regions in the Fermi-Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over 50--80 samples, drastically reduces finite-size effects in some ground-state properties; calculations in the grand-canonical ensemble together with a local-density approximation allow us to simulate the radial density distribution. We have found that as the trap closes, the atomic cloud goes from a metallic state to a Mott core and to a Mott ring; the coverage of Mott atoms reaches a maximum at the core-ring transition. A ``phase diagram'' in terms of an effective density and of the on-site repulsion is proposed as a guide to maximize the Mott coverage. We also predict that the usual experimentally accessible quantities, the global compressibility and the average double occupancy (rather, its density derivative), display detectable signatures of the core-ring transition. Some spin-correlation functions are also calculated and predict the existence N\'eel-like ordering within Mott cores and rings.
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-insulating 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.
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. We show that this model displays quantum critical behavior at the boundaries of the local Mott‐insulating regions. A local compressibility defined to characterize the Mott‐insulating phase has a non‐trivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We study the momentum distribution function and we find that it is not appropriate to characterize the transitions in the system.
We study Mott transition in the two-dimensional Hubbard model on an anisotropic triangular lattice. We use the Lanczos exact diagonalization of finite-size clusters up to eighteen sites, and calculate Drude weight, charge gap, double occupancy and spin structure factor. We average these physical quantities over twisted boundary conditions in order to reduce finite-size effects. We find a signature of the Mott transition in the dependence of the Drude weight and/or charge gap on the system size. We also examine the possibility of antiferromagnetic order from the spin structure factor. Combining these information, we propose a ground-state phase diagram which has a nonmagnetic insulating phase between a metallic phase and an insulating phase with antiferromagnetic order. Finally, we compare our results with those reported in the previous theoretical studies, and discuss the possibility of an unconventional insulating state.
Using quantum Monte Carlo simulations, we show that the one-dimensional fermionic Hubbard model in a harmonic potential displays quantum critical behavior at the boundaries of a Mott-insulating region. A local compressibility defined to characterize the Mott-insulating phase has a nontrivial critical exponent. Both the local compressibility and the variance of the local density show universality with respect to the confining potential. We determine a generic phase diagram, which allows the prediction of the phases to be observed in experiments with ultracold fermionic atoms trapped on optical lattices.
We study the ground-state properties of spin-1/2 fermionic atoms confined in a one-dimensional optical superlattice with harmonic confinement by using the density-matrix renormalization group method. For this purpose, we consider an ionic Hubbard model that has superlattice potentials with two-site periodicity. We find that several different types of insulating regimes coexist even if the number of atoms at each site is not an integer, but its average within the unit cell is an integer or half integer. This is contrasted to the coexisting phase of the metallic and Mott-insulating regimes known for the ordinary Hubbard model in an optical lattice. The phase characteristics are elucidated by investigating the profiles of the atom density, the local density (spin) fluctuations, the double occupation probability, and the spin correlations in detail.