Studies of systems with two fermionic bands with repulsive interaction strength U have a long history, with the Periodic Anderson Model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use Quantum Monte Carlo to study analogous issues for attractive interactions. As in the Periodic Anderson Model, we focus on a case where one band is uncorrelated (U=0), and focus on the effect of hybridization V between the bands on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are able to explore the physics of doped multi-band attractive systems at low temperatures whereas ground state properties of repulsive models can be determined only at half-filling. For small V, pairing in the U<0 layer induces pairing in the U=0 layer. At larger V the ground state of the coupled system loses its superconducting character. The Quantum Monte Carlo data are complemented by results obtained with the Bogoliubov-de Gennes approximation.
Studies of systems with two fermionic bands (or equivalently, layers) with repulsive interaction strength U have a long history, with the periodic Anderson model (PAM) being one of the most frequently considered Hamiltonians. In this paper, we use quantum Monte Carlo to study analogous issues for attractive interactions. As in the PAM, we focus on a case where one band (layer) is uncorrelated ( U = 0), and the effect of hybridization V between the bands (layers) on the pairing correlations. A key difference with the PAM is that there is no sign problem, so that we are better able to explore the physics of doped bilayer attractive systems at low temperatures (except in the case of exponentially small transition temperatures) whereas ground state properties of repulsive models can be determined only at half-filling. For small V , pairing in the U < 0 layer induces pairing in the U = 0 layer. At larger V superfluidity is suppressed at the low but finite T at which the quantum Monte Carlo was performed. The quantum Monte Carlo data are complemented by results obtained with the Bogoliubov–de Gennes approximation.
Motivated by recent experiments realizing correlated phenomena and superconductivity in two-dimensional (2D) van der Waals devices, we consider the general problem of whether correlation effects may be enhanced by modifying band structure while keeping a fixed weak interaction strength. Using determinantal quantum Monte Carlo, we study the 2D Hubbard model for two different band structures: a regular nearest-neighbor tight-binding model and a partially flat-band structure containing a nondispersing region, with identical total noninteracting bandwidth
Wtot. For both repulsive and attractive weak interactions ($|U|\ensuremath{\ll}{W}_{\mathrm{tot}}$), correlated phenomena are significantly stronger in the partially flat model. In the repulsive case, even with
U being an order of magnitude smaller than
Wtot, we find the presence of a Mott insulating state near half filling of the flat region in momentum space. In the attractive case, where generically the ground state is superconducting, the partially flat model exhibits significantly enhanced superconducting transition temperatures. These results suggest the possibility of engineering correlation effects in materials by tuning the noninteracting electronic dispersion.
We present, in this dissertation, a numerical simulation method to study interacting fermion systems. The general simulation procedures are discussed in connection with a description of a Quantum Monte Carlo simulation algorithm for interacting electrons on lattices. The algorithm presented here has been used to simulate interacting electrons on lattices, and it makes possible the study of substantially larger systems than can be studied by other numerical methods. As long as certain limits of applicability are respected, model Hamiltonians of interacting electrons can be studied without resort to uncontrolled approximations. The method then provides nearly exact solutions to model Hamiltonians of many-body systems, in the sense that the degree of error can be controlled. We also discuss some results obtained from simulations of the extended Hubbard model and and the periodic Anderson model. For the extended Hubbard model in two dimensions, different regions are identified where electron correlation produces antiferromagnetism, charge-density-waves, and singlet pairing superconducting behaviors. We also find regions where transitions from one type of correlation to another occur. For the symmetric periodic Anderson model, we observe the formation of local spin moments at high temperatures and their quenching at low temperatures, as in the single impurity Anderson model. In addition, we find antiferromagnetic interaction between f local moments at low temperatures which are not present in a single impurity problem.
The phase diagram for spin 1/2 fermions with attractive interband interactions (- V ) is obtained for the two-band Hubbard model in the space of - V , intraband repulsion ( U ), and the band filling from the quantum Monte Carlo calculation along with the mean-field theory in one dimension. The competition of an off-diagonal long-range order with diagonal orders (CDW and SDW) is shown to result in a superconducting ground state arising from interband pairing (i) in the presence of U of right magnitude ( ∼ V ) and (ii) in non-half-filled bands.
The determinant quantum Monte Carlo (DQMC) method is used to study the effect of nonzero hopping
tf in the ``localized''
f band of the periodic Anderson model (PAM) in two dimensions. The low-temperature properties are determined in the plane of interband hybridization
V and
tf at fixed
Uf and half filling, including the case when the sign of
tf is opposite to that of the conduction band
td. For
tf and
td of the same sign and when
tf/td>(V/4td)2, the noninteracting system is metallic. We show that a remnant of the band insulator to metal line at
Uf=0 persists in the interacting system, manifesting itself as a maximal tendency toward antiferromagnetic correlations at low temperature. In this ``optimal''
tf region, short-range (e.g., near-neighbor) and long-range spin correlations develop at similar temperatures and have comparable magnitude. Both observations are in stark contrast to the situation in the widely studied PAM (
tf=0) and single-band Hubbard model, where short-range correlations are stronger and develop at higher temperature. The effect that finite
tf has on Kondo screening is investigated by considering the evolution of the local density of states for selected
tf as a function of
V. We use mean-field theory as a tool to discriminate those aspects of the physics that are genuinely many-body in character.
We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-
Tc superconductivity in oxides are discussed.