Disorder and superconductivity : a new phase of bi-particle localized states

We study the two-dimensional, disordered, attractive Hubbard model by the projector quantum Monte Carlo method and Bogoliubov - de Gennes mean-field theory. Our results for the ground state show the appearance of a new phase with charge localization in the metallic regime of the non-interacting model. Contrary to the common lore, we demonstrate that mean-field theory fails to predict this phase and is unable to describe the correct physical picture in this regime.Comment: revtex, 4 pages, 3 figure

Variational Monte Carlo and Configurational Interaction Studies of C60C_{60} and its Fragments

The $C_{60}$ molecule and its fragments are studied using Configuration Interaction (CI) and Variational Monte Carlo (VMC) techniques, within the Hubbard model. Using benzene as a test case, we compare the results of the approximate calculations with exact calculations. The fragments of $C_{60}$ studied are pyracylene, fluoranthene and corannulene. The energies, bond orders, spin-spin and charge-correlation functions of these systems are obtained for various values of the Hubbard parameter, $U$. The analysis of bond orders and correlation functions of these individual molecules allow us to visualise pyracylene as a naphthalene unit with two ethylenic moieties and fluoranthene as weakly bridged benzene and naphthalene units. Corannulene is the largest fragment of $C_{60}$ that we have studied. The hexagon-hexagon(h-h) bond orders are slightly larger than those of the hexagon-pentagon bonds(h-p), a feature also found in other fragments. We also find bonds between two co-ordinated carbon sites to be stronger than bonds involving three coordinated carbon sites. In $C_{60}$, the h-h bonds are stronger than in corannulene and the h-p bonds weaker than in corannulene for all correlation strengths. Introducing bond alternation in the buckyball enhances this difference.Comment: 42 pages, 5 figures available on request, to appear in J. Phys. Che

Transition to an Insulating Phase Induced by Attractive Interactions in the Disordered Three-Dimensional Hubbard Model

We study numerically the interplay of disorder and attractive interactions for spin-1/2 fermions in the three-dimensional Hubbard model. The results obtained by projector quantum Monte Carlo simulations show that at moderate disorder, increasing the attractive interaction leads to a transition from delocalized superconducting states to the insulating phase of localized pairs. This transition takes place well within the metallic phase of the single-particle Anderson model.Comment: revtex, 4 pages, 3 figure

Estimation of properties of low-lying excited states of Hubbard models : a multi-configurational symmetrized projector quantum Monte Carlo approach

We present in detail the recently developed multi-configurational symmetrized projector quantum Monte Carlo (MSPQMC) method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo method for a multi-configurational trial wavefunction. We give a detailed discussion of issues related to the symmetry of the projection procedure which validates our Monte Carlo procedure for excited states and leads naturally to the idea of symmetrized sampling for correlation functions, developed earlier in the context of ground state simulations. It also leads to three possible averaging schemes. We have analyzed the errors incurred in these various averaging procedures and discuss and detail the preferred averaging procedure for correlations that do not have the full symmetry of the Hamiltonian. We study the energies and correlation functions of the low-lying excited states of the half-filled Hubbard model in 1-D. We have used this technique to study the pair-binding energies of two holes in $4n$ and $4n+2$ systems, which compare well the Bethe ansatz data of Fye, Martins and Scalettar. We have also studied small clusters amenable to exact diagonalization studies in 2-D and have reproduced their energies and correlation functions by the MSPQMC method. We identify two ways in which a multiconfigurational trial wavefunction can lead to a negative sign problem. We observe that this effect is not severe in 1-D and tends to vanish with increasing system size. We also note that this does not enhance the severity of the sign problem in two dimensions.Comment: 29 pages, 2 figures available on request, submitted to Phys. Rev.

Structural Instability in Polyacene : A Projector Quantum Monte Carlo Study

We have studied polyacene within the Hubbard model to explore the effect of electron correlations on the Peierls' instability in a system marginally away from one-dimension. We employ the projector quantum Monte Carlo method to obtain ground state estimates of the energy and various correlation functions. We find strong similarities between polyacene and polyacetylene which can be rationalized from the real-space valence-bond arguments of Mazumdar and Dixit. Electron correlations tend to enhance the Peierls' instability in polyacene. This enhancement appears to attain a maximum at $U/t \sim 3.0$ and the maximum shifts to larger values when the alternation parameter is increased. The system shows no tendency to destroy the imposed bond-alternation pattern, as evidenced by the bond-bond correlations. The cis- distortion is seen to be favoured over the trans- distortion. The spin-spin correlations show that undistorted polyacene is susceptible to a SDW distortion for large interaction strength. The charge-charge correlations indicate the absence of a CDW distortion for the parameters studied.Comment: 13 pages, 10 figures available on reques

Delocalizing effect of the Hubbard repulsion for electrons on a two-dimensional disordered lattice

We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate values of the ground-state charge density distributions with $N_p$ and $N_p+1$ particles. The difference in these charge densities allows us to study the localization properties of an added particle. The results obtained at quarter-filling on finite clusters show that the Hubbard repulsion has a strong delocalizing effect on the electrons in disordered 2D lattices. However, numerical restrictions do not allow us to reach a definite conclusion about the existence of a metal-insulator transition in the thermodynamic limit in two-dimensions.Comment: revtex, 7 pages, 7 figure

Ground state properties of the 2D disordered Hubbard model

We study the ground state of the two-dimensional (2D) disordered Hubbard model by means of the projector quantum Monte Carlo (PQMC) method. This approach allows us to investigate the ground state properties of this model for lattice sizes up to $10 \times 10$, at quarter filling, for a broad range of interaction and disorder strengths. Our results show that the ground state of this system of spin-1/2 fermions remains localised in the presence of the short-ranged Hubbard interaction.Comment: 7 pages, 9 figure

Transition to an Insulating Phase Induced by Attractive Interactions in the Disordered Three-Dimensional Hubbard Model

We study numerically the interplay of disorder and attractive interactions for spin-1/2 fermions in the three-dimensional Hubbard model. The results obtained by projector quantum Monte Carlo simulations show that at moderate disorder, increasing the attractive interaction leads to a transition from delocalized superconducting states to the insulating phase of localized pairs. This transition takes place well within the metallic phase of the single-particle Anderson model.Comment: revtex, 4 pages, 3 figure

Structural and Electronic Instabilities in Polyacenes: Density Matrix Renormalization Group Study of a Long--Range Interacting Model

We have carried out Density Matrix Renormalization Group (DMRG) calculations on the ground state of long polyacene oligomers within a Pariser-Parr-Pople (PPP) Hamiltonian. The PPP model includes long-range electron correlations which are required for physically realistic modeling of conjugated polymers. We have obtained the ground state energy as a function of the dimerization $\delta$ and various correlation functions and structure factors for $\delta=0$. From energetics, we find that while the nature of the Peierls' instabilityin polyacene is conditional and strong electron correlations enhance the dimerization. The {\it cis} form of the distortion is favoured over the {\it trans} form. However, from the analysis of correlation functions and associated structure factors, we find that polyacene is not susceptible to the formation of a bond order wave (BOW), spin density wave (SDW) or a charge density wave (CDW) in the ground state.Comment: 31 pages, latex, 13 figure