Browsing by Subject "Hubbard model"

Now showing 1 - 4 of 4

Open Access
Effect of disorder on the interacting fermi gases in a one-dimensional optical lattice
(World Scientific Publishing Co., 2008) Xianlong, G.; Polini, M.; Tosi, M. P.; Tanatar, Bilal
Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator and/or band-insulator regions. Motivated by experiments on cold atoms inside disordered optical lattices, we present a theoretical study of the effects of a correlated random potential on these ground-state phases. We employ a lattice version of density-functional theory within the local-density approximation to determine the density distribution of fermions in these phases. The exchange-correlation potential is obtained from the Lieb-Wu exact solution of Fermi-Hubbard model. On-site disorder (with and without Gaussian correlations) and harmonic trap are treated as external potentials. We find that disorder has two main effects: (i) it destroys the local insulating regions if it is suffciently strong compared with the on-site atom-atom repulsion, and (ii) it induces an anomaly in the inverse compressibility at low density from quenching of percolation. For suffciently large disorder correlation length the enhancement in the inverse compressibility diminishes.
Open Access
Existence of a metallic phase in a 1D Holstein-Hubbard model at half filling
(Elsevier B.V., 2007) Krishna, P. M.; Chatterjee, A.
The one-dimensional half-filled Holstein-Hubbard model is studied using a series of canonical transformations including phonon coherence effect that partly depends on the electron density and is partly independent and also incorporating the on-site and the nearest-neighbour phonon correlations and the exact Bethe-ansatz solution of Lieb and Wu. It is shown that choosing a better variational phonon state makes the polarons more mobile and widens the intermediate metallic region at the charge-density-wave-spin-density-wave crossover recently predicted by Takada and Chatterjee. The presence of this metallic phase is indeed a favourable situation from the point of view of high temperature superconductivity.
Open Access
Mean-field renormalization group theory of the t-J model
(2002) Şen, Cengiz
The quantum nature of the high temperature superconductivity models makes analytical approaches to these systems almost impossible to implement. In this thesis, a computational study of the one and two dimensional t − J models that combines mean-field treatments with renormalization group techniques will be presented. This allows one to deal with the noncommutations of the operators at two consecutive sites of the lattices on which these models are defined. The resulting phase diagram for the 1D t − J model reveals an antiferromagnetic ground state, which may, upon doping with increasing temperature, show striped formation that is seen in the high-Tc cuprates. The qualitative features of the phase diagram of the 2D case is also presented, which reveals a phase transition between the disordered and antiferomagnetically ordered phases.
Open Access
Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
(American Physical Society, 2019) Hetenyi, Balazs; Martelo, L. M.; Tanatar, Bilal
We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model with focus on the strong-coupling regime via variational, exact diagonalization, and strong coupling calculations. Our variational approach is based on the Baeriswyl wave function, implemented via Monte Carlo sampling. We derive the superfluid weight appropriately in a variational setting. We emphasize the importance of implementing the Peierls phase in position space and to allow for many-body interference effects, rather than implementing the Peierls phase as single particle momentum shifts. At integer filling, the Baeriswyl wave function gives zero superfluid response at any coupling. At half filling our variational superfluid weight is in reasonable agreement with exact diagonalization results. We also calculate the polarization amplitude, the variance of the total position, and the associated size scaling exponent, which corroborate that this variational approach produces an insulating state at integer filling. Our Baeriswyl based variational method is applicable to significantly larger system sizes than exact diagonalization or quantum Monte Carlo.