arXiv subjects

Emanuel Gull

Publications and source records attributed to Emanuel Gull.

At least 127 records · Page 7Linked to original sources

arXiv2014

Green's functions from real-time bold-line Monte Carlo: spectral properties of the nonequilibrium Anderson impurity model

The nonequilibrium spectral properties of the Anderson impurity model with a chemical potential bias are investigated within a numerically exact real time quantum Monte Carlo formalism. The two-time correlation function is computed in a form suitable for nonequilibrium dynamical mean field calculations. Additionally, the evolution of the model's spectral properties are simulated in an alternative representation, defined by a hypothetical but experimentally realizable weakly coupled auxiliary lead. The voltage splitting of the Kondo peak is confirmed and the dynamics of its formation after a coupling or gate quench are studied. This representation is shown to contain additional information about the dot's population dynamics. Further, we show that the voltage-dependent differential conductance gives a reasonable qualitative estimate of the equilibrium spectral function, but significant qualitative differences are found including incorrect trends and spurious temperature dependent effects.

cond-mat.str-el↗

arXiv2014

Green's functions from real-time bold-line Monte Carlo

We present two methods for computing two-time correlation functions or Green's functions from real time bold-line continuous time quantum Monte Carlo. One method is a formally exact generalized auxiliary lead formalism by which spectral properties may be obtained from single-time observables. The other involves the evaluation of diagrams contributing to two-time observables directly on the Keldysh contour. Additionally, we provide a detailed description of the bold-line Monte Carlo method. Our methods are general and numerically exact, and able to reliably resolve high-energy features such as band edges. We compare the spectral functions obtained from real time methods to analytically continued spectral functions obtained from imaginary time Monte Carlo, thus probing the limits of analytic continuation.

cond-mat.str-el↗

arXiv2014

A comparative DMFT study of the eg-orbital Hubbard model in thin films

Heterostructures of transition-metal oxides emerged as a new route to engineer electronic systems with desired functionalities. Motivated by these developments, we study a two-orbital Hubbard model in a thin-film geometry confined along the cubic [001] direction using the dynamical mean-field theory. We contrast the results of two approximate impurity solvers (exact diagonalization and one-crossing approximation) to the results of the numerically exact continuous-time quantum Monte Carlo solver. Consistent with earlier studies, we find that the one-crossing approximation performs well in the insulating regime, while the advantage of the exact-diagonalization based solver is more pronounced in the metallic regime. We then investigate various aspects of strongly correlated eg-orbital systems in thin film geometries. In particular, we show how the interfacial orbital polarization dies off quickly a few layers from the interface and how the film thickness affects the location of the interaction-driven Mott transition. In addition, we explore the changes in the electronic structure with varying carrier concentration and identify large variations of the orbital polarization in the strongly correlated regime.

cond-mat.str-el↗

arXiv2013

Equation of State of the Fermionic 2D Hubbard Model

We present results for the equation of state of the two-dimensional Hubbard model on an isotropic square lattice as obtained from a controlled and numerically exact large-cluster dynamical mean field simulation. Our results are obtained for large but finite systems and are extrapolated to infinite system size using a known finite size scaling relation. We present the energy, entropy, double occupancy and nearest-neighbour spin correlations extrapolated to the thermodynamic limit and discuss the implications of these calculations on pseudogap physics of the 2D-Hubbard model away from half filling. We find a strong behavioural shift in energy below a temperature $T^*$ which becomes more pronounced for larger clusters. Finally, we provide reference calculations and tables for the equation of state for values of doping away from half filling which are of interest to cold atom experiments.

cond-mat.str-el↗

arXiv2013

Thermodynamics and magnetic properties of the anisotropic 3D Hubbard model

We study the 3D Hubbard model with anisotropic nearest neighbor tunneling amplitudes using the dynamical cluster approximation and compare the results with a quantum simulation experiment using ultracold fermions in an optical lattice, focussing on magnetic correlations. We find that the short-range spin correlations are significantly enhanced in the direction with stronger tunneling amplitudes. Our results agree with the experimental observations and show that the experimental temperature is lower than the strong tunneling amplitude. We characterize the system by examining the spin correlations beyond neighboring sites and determine the distribution of density, entropy and spin correlation in the trapped system. We furthermore investigate the dependence of the critical entropy at the Néel transition on anisotropy.

cond-mat.quant-gas↗

arXiv2013

Superconductivity and the Pseudogap in the two-dimensional Hubbard model

Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. $d_{x^2-y^2}$ symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.

cond-mat.str-el↗

arXiv2013

Superconducting and Pseudogap effects on the interplane conductivity and Raman scattering cross section in the two dimensional Hubbard Model

Cluster dynamical mean field methods are used to calculate the superconductivity-induced changes in the interplane conductivity and Raman scattering cross section of the two dimensional Hubbard model. When superconductivity emerges from the pseudogap, the superconducting response is found to be diminished in amplitude, broadened and, in the case of the interplane conductivity, shifted to higher frequency. The results are in agreement with data on high temperature copper-oxide superconductors indicating that the Hubbard model contains the essential low energy physics of the pseudogap and its interplay with superconductivity in the cuprates.

cond-mat.str-el↗

arXiv2013

Sum rule violation in self-consistent hybridization expansions

We show that for multi-orbital quantum impurity models the non-crossing approximation and one-crossing approximation versions of the self-consistent hybridization expansions violate the sum rules relating the coefficients of the high-frequency expansion of the self energy and the product of the self energy and Green function to thermodynamic expectation values. Comparison of non-crossing/one-crossing results to numerically exact quantum Monte-Carlo calculations shows that the consistency with sum rules provides a useful estimate of the reliability of the approximations. The sum rule violations are more pronounced, and therefore the quality of the non-crossing/one-crossing approximation is poorer, in situations with multiple orbitals and away from particle-hole symmetry but becomes less severe as the correlation strength increases. The one crossing approximation is markedly superior to the non-crossing approximation.

cond-mat.str-el↗

arXiv2013

Efficient implementation of the continuous-time hybridization expansion quantum impurity solver

Strongly correlated quantum impurity problems appear in a wide variety of contexts ranging from nanoscience and surface physics to material science and the theory of strongly correlated lattice models, where they appear as auxiliary systems within dynamical mean-field theory. Accurate and unbiased solutions must usually be obtained numerically, and continuous-time quantum Monte Carlo algorithms, a family of algorithms based on the stochastic sampling of partition function expansions, perform well for such systems. With the present paper we provide an efficient and generic implementation of the hybridization expansion quantum impurity solver, based on the segment representation. We provide a complete implementation featuring most of the recently developed extensions and optimizations. Our implementation allows one to treat retarded interactions and provides generalized measurement routines based on improved estimators for the self-energy and for vertex functions. The solver is embedded in the ALPS-DMFT application package.

cond-mat.str-el↗

arXiv2012

Energetics of superconductivity in the two dimensional Hubbard model

The energetics of the interplay between superconductivity and the pseudogap in high temperature superconductivity is examined using the eight-site dynamical cluster approximation to the two dimensional Hubbard model. Two regimes of superconductivity are found: a weak coupling/large doping regime in which the onset of superconductivity causes a reduction in potential energy and an increase in kinetic energy, and a strong coupling regime in which superconductivity is associated with an increase in potential energy and decrease in kinetic energy. The crossover between the two regimes is found to coincide with the boundary of the normal state pseudogap, providing further evidence of the unconventional nature of superconductivity in the pseudogap regime. However the absence, in the strongly correlated but non-superconducting state, of discernibly nonlinear response to an applied pairing field, suggests that resonating valence bond physics is not the origin of the kinetic-energy driven superconductivity.

cond-mat.str-el↗

arXiv2012

Numerically Exact Long Time Magnetization Dynamics at the Nonequilibrium Kondo Crossover of the Anderson Impurity Model

We investigate the dynamical and steady-state spin response of the nonequilibrium Anderson model to magnetic fields, bias voltage, and temperature using a numerically exact method combining a bold-line quantum Monte Carlo technique with the memory function formalism. We obtain converged results in a range of previously inaccessible regimes, in particular the crossover to the Kondo domain. We provide detailed predictions for novel nonequilibrium phenomena, including non-monotonic temperature dependence of observables at high bias voltage and oscillatory quench dynamics at high magnetic fields.

cond-mat.str-el↗

arXiv2012

Two-particle response in Cluster Dynamical Mean-Field Theory: Formalism and application to the Raman Response of High-temperature Superconductors

A method is presented for the unbiased numerical computation of two-particle response functions of correlated electron materials via a solution of the dynamical mean-field equations in the presence of a perturbing field. The power of the method is demonstrated via a computation of the Raman $B_{1g}$ and $B_{2g}$ scattering intensities of the two dimensional Hubbard model, in parameter regimes believed to be relevant to high-temperature superconductivity. The theory reproduces the `two-magnon' peak characteristic of the Raman intensity of the insulating parent compounds of high-$T_c$ copper oxide superconductors and shows how it evolves to a quasiparticle response as carriers are added. The method can be applied in any situation where a solution of the equilibrium dynamical mean-field equations is feasible.

cond-mat.str-el↗

arXiv2012

Truncated Configuration Interaction expansions as solvers for correlated quantum impurity models and dynamical mean field theory

The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nano-science to the dynamical mean-field theory (DMFT). Here we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the 1D Hubbard model and $2\times 2$ cluster DMFT of the 2D Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including "difficult" regimes, such as in the pseudogap phase of the 2D Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\times 2$ cluster DMFT using a 24 bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.

cond-mat.str-el↗

arXiv2011

Superconductivity and Pairing Fluctuations in the Half-Filled Two-Dimensional Hubbard Model

The two-dimensional Hubbard model exhibits superconductivity with d-wave symmetry even at half-filling in the presence of next-nearest neighbor hopping. Using plaquette cluster dynamical mean-field theory with a continuous-time quantum Monte Carlo impurity solver, we reveal the non-Fermi liquid character of the metallic phase in proximity to the superconducting state. Specifically, the low-frequency scattering rate for momenta near (π, 0) varies non-monotonously at low temperatures, and the dc conductivity is T-linear at elevated temperatures with an upturn upon cooling. Evidence is provided that pairing fluctuations dominate the normal-conducting state even considerably above the superconducting transition temperature.

cond-mat.str-el↗

arXiv2011

Charge and spin criticality for the continuous Mott transition in a two-dimensional organic conductor

We study the continuous bandwidth-controlled Mott transition in the two-dimensional single-band Hubbard model with a focus on the critical scaling behavior of charge and spin degrees of freedom. Using plaquette cluster dynamical mean-field theory, we find charge and spin criticality consistent with experimental results for organic conductors. In particular, the charge degree of freedom measured via the local density of states at the Fermi level shows a smoother transition than expected for the Ising universality class and in single-site dynamical mean-field theory, revealing the importance of short-ranged nonlocal correlations in two spatial dimensions. The spin criticality measured via the local spin susceptibility agrees quantitatively with nuclear magnetic resonance measurements of the spin-lattice relaxation rate.

cond-mat.str-el↗

arXiv2011

Spectral properties of the three-dimensional Hubbard model

We present momentum resolved single-particle spectra for the three-dimensional Hubbard model for the paramagnetic and antiferromagnetically ordered phase obtained within the dynamical cluster approximation. The effective cluster problem is solved by continuous-time Quantum Monte Carlo simulations. The absence of a time discretization error and the ability to perform Monte Carlo measurements directly in Matsubara frequencies enable us to analytically continue the self-energies by maximum entropy, which is essential to obtain momentum resolved spectral functions for the N'eel state. We investigate the dependence on temperature and interaction strength and the effect of magnetic frustration introduced by a next-nearest neighbor hopping. One particular question we address here is the influence of the frustrating interaction on the metal insulator transition of the three-dimensional Hubbard model.

cond-mat.str-el↗

arXiv2011

Sub-matrix updates for the Continuous-Time Auxiliary Field algorithm

We present a sub-matrix update algorithm for the continuous-time auxiliary field method that allows the simulation of large lattice and impurity problems. The algorithm takes optimal advantage of modern CPU architectures by consistently using matrix instead of vector operations, resulting in a speedup of a factor of $\approx 8$ and thereby allowing access to larger systems and lower temperature. We illustrate the power of our algorithm at the example of a cluster dynamical mean field simulation of the Néel transition in the three-dimensional Hubbard model, where we show momentum dependent self-energies for clusters with up to 100 sites.

cond-mat.str-el↗

arXiv2011

Numerically Exact Long Time Behavior of Nonequilibrium Quantum Impurity Models

A Monte Carlo sampling of diagrammatic corrections to the non-crossing approximation is shown to provide numerically exact estimates of the long-time dynamics and steady state properties of nonequilibrium quantum impurity models. This `bold' expansion converges uniformly in time and significantly ameliorates the sign problem that has heretofore limited the power of real-time Monte Carlo approaches to strongly interacting real-time quantum problems. The new approach enables the study of previously intractable problems ranging from generic long time nonequilibrium transport characteristics in systems with large onsite repulsion to the direct description of spectral functions on the real frequency axis in Dynamical Mean Field Theory.

cond-mat.str-el↗