1,721,018 research outputs found
Analytic continuation of quantum Monte Carlo data by stochastic analytical inference
No full textWe present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation
Quantum cluster theories
No full textThis article reviews quantum cluster theories, a set of approximations for infinite lattice models which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a mean-field approximation. These methods become exact when the cluster size diverges, and most recover the corresponding mean-field approximation when the cluster size becomes 1. Although quantum cluster theories were originally developed to treat disordered systems, they have more recently been applied to the study of ordered and disordered correlated systems, which will be the focus of this review. After a brief historical review, the authors provide detailed derivations of three cluster formalisms: the cluster perturbation theory, the dynamical cluster approximation, and the cellular dynamical mean-field theory. They compare their advantages and review their applications to common models of correlated electron systems
Unconventional Superconductivity from Local Spin Fluctuations in the Kondo Lattice
No full textThe explanation of heavy-fermion superconductivity is a long-standing challenge to theory. It is commonly thought to be connected to nonlocal fluctuations of either spin or charge degrees of freedom and therefore of unconventional type. Here we present results for the Kondo-lattice model, a paradigmatic model to describe heavy-fermion compounds, obtained from dynamical mean-field theory which captures local correlation effects only. Unexpectedly, we find robust s-wave superconductivity in the heavy-fermion state. We argue that this novel type of pairing is tightly connected to the formation of heavy quasiparticle bands and the presence of strong local spin fluctuations. DOI: 10.1103/PhysRevLett.110.146406DFG [PR293/13-1]; BMBF [IND 10/067, FOR 960, GRK 1621]; ARRS [P1-0044
Efficient calculation of the antiferromagnetic phase diagram of the three-dimensional Hubbard model
No full textThe dynamical cluster approximation (DCA) with Betts clusters is used to calculate the antiferromagnetic phase diagram of the three-dimensional Hubbard model at half-filling. Betts clusters are a set of periodic clusters which best reflect the properties of the lattice in the thermodynamic limit and provide an optimal finite-size scaling as a function of cluster size. Using a systematic finite-size scaling as a function of cluster space-time dimensions, we calculate the antiferromagnetic phase diagram. Our results are qualitatively consistent with the results of Staudt [Eur. Phys. J. B 17, 411 (2000)], but require the use of much smaller clusters: 48 compared to 1000
Imaginary-time quantum many-body theory out of equilibrium. II. Analytic continuation of dynamic observables and transport properties
No full textWithin the imaginary-time theory for nonequilibrium in quantum dot systems the calculation of dynamical quantities like Green's functions is possible via a suitable quantum Monte Carlo algorithm. The challenging task is to analytically continue the imaginary-time data for both complex voltage and complex frequency onto the real variables. To this end a function-theoretical description of dynamical observables is introduced and discussed within the framework of the mathematical theory of several complex variables. We construct a feasible maximum-entropy algorithm for the analytical continuation by imposing a continuity assumption on the analytic structure and provide results for spectral functions in stationary nonequilibrium and current-voltage characteristics for different values of the dot charging energy
Continuous-time quantum Monte Carlo and maximum entropy approach to an imaginary-time formulation of strongly correlated steady-state transport
No full textRecently, Han and Heary [Phys. Rev. Lett. 99, 236808 (2007)] proposed an approach to steady-state quantum transport through mesoscopic structures, which maps the nonequilibrium problem onto a family of auxiliary quantum impurity systems subject to imaginary voltages. We employ continuous-time quantum Monte-Carlo solvers to calculate accurate imaginary time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods
Spectral properties of the three-dimensional Hubbard model
No full textWe 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 obtaining momentum-resolved spectral functions for the Neel 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
Suppression of d-wave superconductivity in the checkerboard Hubbard model
No full textUsing a dynamical cluster quantum Monte Carlo approximation, we investigate the d-wave superconducting transition temperature T(c) in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings t' and t in the form of a checkerboard pattern where t is the hopping within a 2x2 plaquette, and t' is the hopping between the plaquettes. We find inhomogeneity suppresses T(c). The characteristic spin excitation energy and the strength of d-wave pairing interaction decrease with decreasing T(c), suggesting a strong correlation between these quantities
Phonons and the coherence scale of models of heavy fermions
No full textWe consider models of heavy fermions in the strong coupling or local-moment limit and include phonon degrees of freedom on the conduction electrons. Due to the large mass or low coherence temperature of the heavy-fermion state, it is shown that such a regime is dominated by vertex corrections which leads to the complete failure of the Migdal theorem. Even at weak electron-phonon couplings, binding of the conduction electrons competes with the Kondo effect and substantially reduces the coherence temperature, ultimately leading to the Kondo breakdown. Those results are obtained using a combination of the slave-boson method and Migdal-Eliashberg approximation as well as the dynamical mean-field theory approximation
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