K. Bouadim - Academia.edu (original) (raw)
Papers by K. Bouadim
We have examined the behavior of the compressibility, of the DC-conductivity, and of the Drude we... more We have examined the behavior of the compressibility, of the DC-conductivity, and of 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 \times 16 sites. While the compressibility and the DC-conductivity are
Physical Review B, 2007
We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using de... more We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo (DQMC). At half-filling, when the interaction strength or the staggered potential dominate we find Mott and band insulators, respectively. When these two energies are of the same order we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.
Localisation 2011, 2012
It is well known that the metal-insulator transition in two dimensions for noninteracting fermion... more It is well known that the metal-insulator transition in two dimensions for noninteracting fermions takes place at infinitesimal disorder. In contrast, the superconductorto-insulator transition takes place at a finite critical disorder (on the order of Vc ∼ 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 singleparticle 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 singleparticle 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.
Physical Review B, 2012
We have examined the behavior of the compressibility, of the DC-conductivity, and of the Drude we... more We have examined the behavior of the compressibility, of the DC-conductivity, and of 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 × 16 sites. While the compressibility and the DC-conductivity 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.
Physical Review B, 2009
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantu... more 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 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.
Journal of Physics: Conference Series, 2012
In two dimensions there is a direct superconductor-to-insulator quantum phase transition driven b... more 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
ABSTRACT Dynamic Hubbard models describe relaxation of atomic orbitals when electrons are added t... more 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.
We extract the dynamical properties of a disordered s-wave superconductor using a combination of ... more 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
ABSTRACT The superconductor-insulator transition (SIT) is defined, at the most fundamental level,... more 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)
ABSTRACT We study the metal-insulator transition in the repulsive disordered 2D Hubbard model [1,... more 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).
Physical Review Letters, 2007
We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard mode... more 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.
Physical Review Letters, 2009
We study the conductivity, density of states, and magnetic correlations of a two-dimensional, two... more 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.
Physical Review B, 2008
The 'dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repul... more The 'dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant Quantum Monte Carlo method. Our key result is that the extended s-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation.
Physical Review B, 2008
The single band, two dimensional Hubbard Hamiltonian has been extensively studied as a model for ... more The single band, two dimensional Hubbard Hamiltonian has been extensively studied as a model for high temperature superconductivity. While Quantum Monte Carlo simulations within the dynamic cluster approximation are now providing considerable evidence for a d-wave superconducting state at low temperature, such a transition remains well out of reach of finite lattice simulations because of the "sign problem". We show here that a bilayer Hubbard model, in which one layer is electron doped and one layer is hole doped, can be studied to lower temperatures and exhibits an interesting signal of d-wave pairing. The results of our simulations bear resemblance to a recent report on the magnetic and superconducting properties of Ba2Ca3Cu4O8F2 which contains both electron and hole doped CuO2 planes. We also explore the phase diagram of bilayer models in which each sheet is at half-filling.
Page 1. arXiv:0710.1356v1 [cond-mat.supr-con] 6 Oct 2007 Quantum Monte Carlo Study of a Dynamic H... more Page 1. arXiv:0710.1356v1 [cond-mat.supr-con] 6 Oct 2007 Quantum Monte Carlo Study of a Dynamic Hubbard Model K. Bouadim1, M. Enjalran2, F. Hébert1, GG Batrouni1, and RT Scalettar3 1INLN, Université de Nice-Sophia ...
We have examined the behavior of the compressibility, of the DC-conductivity, and of the Drude we... more We have examined the behavior of the compressibility, of the DC-conductivity, and of 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 \times 16 sites. While the compressibility and the DC-conductivity are
Physical Review B, 2007
We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using de... more We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo (DQMC). At half-filling, when the interaction strength or the staggered potential dominate we find Mott and band insulators, respectively. When these two energies are of the same order we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.
Localisation 2011, 2012
It is well known that the metal-insulator transition in two dimensions for noninteracting fermion... more It is well known that the metal-insulator transition in two dimensions for noninteracting fermions takes place at infinitesimal disorder. In contrast, the superconductorto-insulator transition takes place at a finite critical disorder (on the order of Vc ∼ 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 singleparticle 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 singleparticle 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.
Physical Review B, 2012
We have examined the behavior of the compressibility, of the DC-conductivity, and of the Drude we... more We have examined the behavior of the compressibility, of the DC-conductivity, and of 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 × 16 sites. While the compressibility and the DC-conductivity 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.
Physical Review B, 2009
We study the attractive fermionic Hubbard model on a honeycomb lattice using determinantal quantu... more 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 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.
Journal of Physics: Conference Series, 2012
In two dimensions there is a direct superconductor-to-insulator quantum phase transition driven b... more 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
ABSTRACT Dynamic Hubbard models describe relaxation of atomic orbitals when electrons are added t... more 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.
We extract the dynamical properties of a disordered s-wave superconductor using a combination of ... more 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
ABSTRACT The superconductor-insulator transition (SIT) is defined, at the most fundamental level,... more 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)
ABSTRACT We study the metal-insulator transition in the repulsive disordered 2D Hubbard model [1,... more 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).
Physical Review Letters, 2007
We study the transitions from band insulator to metal to Mott insulator in the ionic Hubbard mode... more 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.
Physical Review Letters, 2009
We study the conductivity, density of states, and magnetic correlations of a two-dimensional, two... more 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.
Physical Review B, 2008
The 'dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repul... more The 'dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant Quantum Monte Carlo method. Our key result is that the extended s-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation.
Physical Review B, 2008
The single band, two dimensional Hubbard Hamiltonian has been extensively studied as a model for ... more The single band, two dimensional Hubbard Hamiltonian has been extensively studied as a model for high temperature superconductivity. While Quantum Monte Carlo simulations within the dynamic cluster approximation are now providing considerable evidence for a d-wave superconducting state at low temperature, such a transition remains well out of reach of finite lattice simulations because of the "sign problem". We show here that a bilayer Hubbard model, in which one layer is electron doped and one layer is hole doped, can be studied to lower temperatures and exhibits an interesting signal of d-wave pairing. The results of our simulations bear resemblance to a recent report on the magnetic and superconducting properties of Ba2Ca3Cu4O8F2 which contains both electron and hole doped CuO2 planes. We also explore the phase diagram of bilayer models in which each sheet is at half-filling.
Page 1. arXiv:0710.1356v1 [cond-mat.supr-con] 6 Oct 2007 Quantum Monte Carlo Study of a Dynamic H... more Page 1. arXiv:0710.1356v1 [cond-mat.supr-con] 6 Oct 2007 Quantum Monte Carlo Study of a Dynamic Hubbard Model K. Bouadim1, M. Enjalran2, F. Hébert1, GG Batrouni1, and RT Scalettar3 1INLN, Université de Nice-Sophia ...