[Show abstract][Hide abstract] ABSTRACT: It is well known that the metal-insulator transition in two dimensions for
non-interacting fermions takes place at infinitesimal disorder. In contrast,
the superconductor-to-insulator transition takes place at a finite critical
disorder (on the order of V_c ~ 2t), where V is the typical width of the
distribution of random site energies and t is the hopping scale. In this
article we compare the localization/delocalization properties of one and two
particles. Whereas the metal-insulator transition is a consequence of
single-particle Anderson localization, the superconductor-insulator transition
(SIT) is due to pair localization - or, alternatively, fluctuations of the
phase conjugate to pair density. The central question we address is how
superconductivity emerges from localized single-particle states. We address
this question using inhomogeneous mean field theory and quantum Monte Carlo
techniques and make several testable predictions for local spectroscopic probes
across the SIT. We show that with increasing disorder, the system forms
superconducting blobs on the scale of the coherence length embedded in an
insulating matrix. In the superconducting state, the phases on the different
blobs are coherent across the system whereas in the insulator long-range phase
coherence is disrupted by quantum fluctuations. As a consequence of this
emergent granularity, we show that the single-particle energy gap in the
density of states survives across the transition, but coherence peaks exist
only in the superconductor. A characteristic pseudogap persists above the
critical disorder and critical temperature, in contrast to conventional
theories. Surprisingly, the insulator has a two-particle gap scale that
vanishes at the SIT despite a robust single-particle gap.
[Show abstract][Hide abstract] ABSTRACT: In two dimensions there is a direct superconductor-to-insulator quantum phase transition driven by increasing disorder. We elucidate, using a combination of inhomogeneous mean field theory and quantum Monte Carlo techniques, the nature of the phases and the mechanism of the transition. We make several testable predictions specifically for local spectroscopic probes. With increasing disorder, the system forms superconducting blobs on the scale of the coherence length embedded in an insulating matrix. In the superconducting state, the phases on the different blobs are coherent across the system whereas in the insulator long range phase coherence is disrupted by quantum fluctuations. As a consequence of this emergent granularity, we show that the single-particle energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT, despite a robust single-particle gap.
Journal of Physics Conference Series 07/2012; 376(1). DOI:10.1088/1742-6596/376/1/012001
[Show abstract][Hide abstract] ABSTRACT: We have examined the behavior of the compressibility, the dc-conductivity,
the single-particle gap, and the Drude weight as probes of the density-driven
metal-insulator transition in the Hubbard model on a square lattice. These
quantities have been obtained through determinantal quantum Monte Carlo
simulations at finite temperatures on lattices up to 16 X 16 sites. While the
compressibility, the dc-conductivity, and the gap are known to suffer from
`closed-shell' effects due to the presence of artificial gaps in the spectrum
(caused by the finiteness of the lattices), we have established that the former
tracks the average sign of the fermionic determinant ( ), and that a
shortcut often used to calculate the conductivity may neglect important
corrections. Our systematic analyses also show that, by contrast, the Drude
weight is not too sensitive to finite-size effects, being much more reliable as
a probe to the insulating state. We have also investigated the influence of the
discrete imaginary-time interval (\Delta\tau) on , on the average density
(\rho), and on the double occupancy (d): we have found that and \rho are
more strongly dependent on \Delta \tau away from closed-shell configurations,
but d follows the \Delta\tau^2 dependence in both closed- and open-shell cases.
[Show abstract][Hide abstract] ABSTRACT: The superconductor-insulator transition (SIT) is defined, at the most fundamental level, in terms of electromagnetic response. The Mattis-Bardeen theory for conventional superconductors becomes inadequate near the disorder-tuned SIT, where phase fluctuations become important. We present AC conductivity results obtained using determinant quantum Monte Carlo simulations, which include both quantum and thermal phase fluctuations. We find unexpected low-energy weight in the AC conductivity especially near the SIT, and we identify possible sources of this weight. We comment on implications for experiments [1,2]. [4pt] [1] R. Vald'es Aguilar et al., Phys. Rev. B 82, 180514 (2010)[0pt] [2] I. Hetel et al., Nature Physics 3, 700-702 (2007)
[Show abstract][Hide abstract] ABSTRACT: In spite of decades of research, the mechanism of the disorder- driven superconductor- insulator transition (SIT) and the nature of the insulator are not understood. We use quantum Monte Carlo simulations that treat, on an equal footing, inhomogeneous amplitude variations and phase fluctuations, a major advance over previous theories. The energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT, despite a robust single-particle gap. Our predictions are testable with scanning probe experiments.
[Show abstract][Hide abstract] ABSTRACT: Polarized Fermi gases hold the possibility of an exotic and fragile modulated superfluid known as a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Quasi-one-dimensional systems of ultracold fermions are the ideal place to look for FFLO physics. Using various methods [1] (including determinant quantum Monte Carlo, stochastic Green function, and Bogoliubov-de Gennes methods), we study the correlation functions and quantum dynamics of polarized Fermi gases in single chains and coupled chains. Our results indicate that fluctuating domain walls lead to spectral weight near the Fermi energy in the spin-resolved density of states, that are a signature of Andreev reflections and fluctuating bound states. We derive bounds for the optimal interchain coupling to maximize the critical temperature of the FFLO state, in order to aid detection of these FFLO states in cold atom experiments [2].[4pt] [1] Y.-L. Loh and N. Trivedi, Phys. Rev. Lett. 104, 165302 (2010).[0pt] [2] Y-an. Liao et. al Nature 467, 567-569 (2010).
[Show abstract][Hide abstract] ABSTRACT: We study the metal-insulator transition in the repulsive disordered 2D Hubbard model [1,2] using Determinant Quantum Monte Carlo (DQMC). We calculate the spin-spin and current-current correlations to learn about the nature of the conducting and insulating phases. We also obtain local spin-dependent spectroscopic properties, using the maximum entropy method, to understand the role of disorder on the transition in this highly correlated fermion system. We discuss implications of our results for scanning tunneling spectroscopy and dynamical conductivity experiments [3]. [4pt] [1]. P.J.H Denteneer, R.T. Scalettar and N. Trivedi, Phys. Rev. Lett.83, 4610 (1999).[0pt] [2]. D. Heidarian and N. Trivedi, Phys. Rev. Lett. 93, 126401 (2004).[0pt] [3]. M.M. Qazilbash et. al., Science 318, 1750 (2007).
[Show abstract][Hide abstract] ABSTRACT: The competition between superconductivity and localization raises profound
questions in condensed matter physics. In spite of decades of research, the
mechanism of the superconductor-insulator transition (SIT) and the nature of
the insulator are not understood. We use quantum Monte Carlo simulations that
treat, on an equal footing, inhomogeneous amplitude variations and phase
fluctuations, a major advance over previous theories. We gain new microscopic
insights and make testable predictions for local spectroscopic probes. The
energy gap in the density of states survives across the transition, but
coherence peaks exist only in the superconductor. A characteristic pseudogap
persists above the critical disorder and critical temperature, in contrast to
conventional theories. Surprisingly, the insulator has a two-particle gap scale
that vanishes at the SIT, despite a robust single-particle gap.
[Show abstract][Hide abstract] ABSTRACT: We extract the dynamical properties of a disordered s-wave superconductor using a combination of auxiliary field Quantum Monte Carlo and analytic continuation methods. By comparing with self-consistent Bogoliubov-de Gennes mean field theory for the same disorder realizations, we are able to obtain fundamentally new insights into the roles of amplitude and phase fluctuations across the disorder-driven superconductor-insulator transition. The disordered superconductor is found to self-organize into local superconducting puddles embedded in an insulating matrix [1]. At finite temperature, the density of states shows coherence peaks below Tc, but only a pseudogap above Tc. Finally, we discuss the behavior of both local and global densities of states in connection to recent scanning tunneling spectroscopy experiments in thin superconducting films [2].[4pt] [1] A. Ghosal et al., Phys. Rev. Lett. 81 3940 (1998);Phys. Rev. B 65, 014501 (2001).[0pt] [2] Sacepe et al, Phys. Rev. Lett. 101, 157006 (2008).
[Show abstract][Hide abstract] ABSTRACT: We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantum Monte Carlo simulations. By increasing the interaction strength U (relative to the hopping parameter t) at half filling and zero temperature, the system undergoes a quantum phase transition at 5.0<Uc/t<5.1 from a semimetal to a phase displaying simultaneously superfluid behavior and density order. Doping away from half filling, and increasing the interaction strength at finite but low temperature T, the system always appears to be a superfluid exhibiting a crossover between a BCS and a molecular regime. These different regimes are analyzed by studying the spectral function. The formation of pairs and the emergence of phase coherence throughout the sample are studied as U is increased and T is lowered.
[Show abstract][Hide abstract] ABSTRACT: We study the attractive fermionic Hubbard model on a honeycomb lattice
using determinantal quantum Monte Carlo simulations. By increasing the
interaction strength U (relative to the hopping parameter t) at
half-filling and zero temperature, the system undergoes a quantum phase
transition at 5.0 < U_c/t < 5.1 from a semi-metal to a phase
displaying simultaneously superfluid behavior and density order. Doping
away from half-filling, and increasing the interaction strength at
finite but low temperature T, the system always appears to be a
superfluid exhibiting a crossover between a BCS and a molecular regime.
These different regimes are analyzed by studying the spectral function.
The formation of pairs and the emergence of phase coherence throughout
the sample are studied as U is increased and T is lowered.
[Show abstract][Hide abstract] ABSTRACT: We study the conductivity, density of states, and magnetic correlations of a two-dimensional, two-band fermion Hubbard model using determinant quantum Monte Carlo (DQMC) simulations. We show that an orbitally selective Mott transition (OSMT) occurs in which the more weakly interacting band can be metallic despite complete localization of the strongly interacting band. The DQMC method allows us to test the validity of the use of a momentum independent self-energy which has been a central approximation in previous OSMT studies. In addition, we show that long range antiferromagnetic order (LRAFMO) is established in the insulating phase, similar to the single band, square lattice Hubbard Hamiltonian. Because the critical interaction strengths for the onset of insulating behavior are much less than the bandwidth of the itinerant orbital, we suggest that LRAFMO plays a key role in the transitions.
[Show abstract][Hide abstract] ABSTRACT: We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard model on a two-dimensional square lattice using determinant quantum Monte Carlo. Evaluation of the temperature dependence of the conductivity demonstrates that the metallic region extends for a finite range of interaction values. The Mott phase at strong coupling is accompanied by antiferromagnetic order. Inclusion of these intersite correlations changes the phase diagram qualitatively compared to dynamical mean field theory.
[Show abstract][Hide abstract] ABSTRACT: Dynamic Hubbard models describe relaxation of atomic orbitals when electrons are added to already occupied orbitals, a phenomenon that is not present in the conventional Hubbard model and that may play a role in superconductivity. We use the determinant algorithm to study the properties of a particular dynamic Hubbard model on a two-dimensional square lattice. We report preliminary results for a set of correlation functions, and our data are compared to results from the standard Hubbard model. We find that a dynamic interaction enhances the pair-field susceptibility, signaling the possible on-set of a superconducting phase.