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arXiv:0904.4815 · Physical Review Letters

Hopping Modulation in a One-Dimensional Fermi-Hubbard Hamiltonian

Francesco Massel, M. J. Leskinen, Päivi Törmä

Published Aug 7, 2009• 16 citations
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Abstract

We consider a strongly repulsive two-component Fermi gas in a one-dimensional optical lattice described in terms of a Hubbard Hamiltonian. We analyze the response of the system to a periodic modulation of the hopping amplitude in the presence of a large two-body interaction. By (essentially) the exact simulations of the time evolution, we find a nontrivial double occupancy frequency dependence. We show how the dependence relates to the spectral features of the system given by the Bethe ansatz. The discrete nature of the spectrum is clearly reflected in the double occupancy after a long enough modulation time. We also discuss the implications of the 1D results to experiments in higher dimensional systems.

DOI
10.1103/physrevlett.103.066404

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We consider a strongly repulsive two-component Fermi gas in a one-dimensional optical lattice described in terms of a Hubbard Hamiltonian. We analyze the response of the system to a periodic modulation of the hopping amplitude in the presence of a large two-body interaction. By (essentially) the exact simulations of the time evolution, we find a nontrivial double occupancy frequency dependence. We show how the dependence relates to the spectral features of the system given by the Bethe ansatz. The discrete nature of the spectrum is clearly reflected in the double occupancy after a long enough modulation time. We also discuss the implications of the 1D results to experiments in higher dimensional systems.
We perform a numerical study of a one-dimensional Fermi-Hubbard model in harmonic traps within the Thomas-Fermi approximation based on the exact Bethe-ansatz solution. The $\ensuremath{\rho}\ensuremath{-}U/t$ phase diagram is shown for the systems of attractive interactions ($\ensuremath{\rho}$ is the characteristic density and U/tU/tU/t the interaction strength scaled in units of the hopping parameter). We study the double occupancy, the local central density, and their derivatives. Their roles in detecting the composite phases induced by the trapping potential are discussed in detail.
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.
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Fermionic atoms in a periodic optical lattice provide a realization of the single-band Hubbard model. Using quantum Monte Carlo simulations along with the maximum-entropy method, we evaluate the effect of a time-dependent perturbative modulation of the optical lattice amplitude on atomic correlations, revealed in the fraction of doubly occupied sites. We find that the effect of modulation depends strongly on the filling---the response of the double occupation is significantly different in the half-filled Mott insulator from that in the doped Fermi liquid region.
Recent experiments show that periodic modulations of cold atoms in optical lattices may be used to engineer and explore interesting models. We show that double modulation combining lattice shaking and modulated interactions allows for the engineering of a much broader class of lattice with correlated hopping, which we study for the particular case of one-dimensional systems. We show, in particular, that by using this double modulation it is possible to study Hubbard models with asymmetric hopping, which, contrary to the standard Hubbard model, present insulating phases with both parity and string order. Moreover, double modulation allows for the simulation of lattice models in unconventional parameter regimes, as we illustrate for the case of the spin-1/2 Fermi-Hubbard model with correlated hopping, a relevant model for cuprate superconductors.
Two fermions occupying the same site of a lattice model with strongly repulsive Hubbard-type interaction UUU form a doublon, a long-living excitation, the decay of which is suppressed because of energy conservation. By means of an exact-diagonalization approach based on the Krylov-space technique, we study the dynamics of a single doublon, of two doublons, and of a doublon in the presence of two additional fermions prepared locally in the initial state of the extended Hubbard model. The time dependence of the expectation value of the double occupancy at the different sites of a large one-dimensional lattice is analyzed by perturbative arguments. In this way the spatiotemporal evolution of the doublon can be understood. The initial decay takes place on a short time scale 1/U1/U1/U, and the long-time average of the decayed fraction of the total double occupancy scales as 1/U21/{U}^{2}1/U2. We demonstrate how the dynamics of a doublon in the initial state is related to the spectrum of two-fermion excitations obtained from linear-response theory, we work out the difference between doublons composed of fermions vs doublons composed of bosons, and we show that despite the increase of phase space for inelastic decay processes, the stability of a doublon is enhanced by the presence of additional fermions on an intermediate time scale.