Solving the parquet equations for the Hubbard model beyond weak coupling.

We find that imposing crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods is limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed time reversal and a subset of the point group symmetries, but they did not further improve the convergence. We elaborate the details of the latency hiding scheme which can significantly improve the performance in the computational implementation. With these modifications, stable solutions for the parquet equations can be obtained by iteration more quickly even for values of the interaction that are a significant fraction of the bandwidth and for temperatures that are much smaller than the bandwidth. This may represent a crucial step towards the solution of two-particle field theories for correlated electron models.

Mean-field embedding of the dual-fermion approach for correlated electron systems.

To reduce the rapidly growing computational cost of the dual-fermion lattice calculation with increasing system size, we introduce two embedding schemes. One is the real fermion embedding, and the other is the dual-fermion embedding. Our numerical tests show that the real fermion and dual-fermion embedding approaches converge to essentially the same result. The application on the Anderson disorder and Hubbard models shows that these embedding algorithms converge more quickly with system size as compared to the conventional dual-fermion method, for the calculation of both single- and two-particle quantities.

Suppression of superconductivity in the Hubbard model by buckling and breathing phonons.

We study the effect of buckling and breathing phonons, relevant for cuprate superconductors, on the d-wave superconductivity in the two-dimensional Hubbard model by employing dynamical cluster Monte Carlo calculations. The interplay of electronic correlations and the electron-phonon interaction produces two competing effects: an enhancement of the effective d-wave pairing interaction, which favors d-wave superconductivity, and a strong renormalization of the single-particle propagator, which suppresses superconductivity. In the region of the parameter space relevant for cuprate superconductors, we find that the buckling and the breathing phonons suppress the superconductivity.

Quantum criticality and incipient phase separation in the thermodynamic properties of the Hubbard model.

Transport measurements on the cuprates suggest the presence of a quantum critical point (QCP) hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single-particle quantities, such as the spectral function, the quasi-particle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudo-gap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbour hopping t', we find a classical critical point at temperature T(c). This classical critical point is found to be associated with a phase-separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudo-gap state, respectively. Since the critical temperature T(c) extrapolates to zero as t' vanishes, we conclude that a QCP connects the Fermi liquid to the pseudo-gap region, and that the marginal Fermi-liquid behaviour in its vicinity is the analogue of the supercritical region in the liquid-gas transition.

Proximity of the superconducting dome and the quantum critical point in the two-dimensional Hubbard model.

We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, T(c) may be enhanced through an increase in the d-wave pairing interaction (V(d)) or the bare pairing susceptibility (χ(0d)). At optimal doping, where V(d) is revealed to be featureless, we find a power-law behavior of χ(0d)(ω=0), replacing the BCS log, and strongly enhanced T(c). We suggest experiments to verify our predictions.

Cluster solver for dynamical mean-field theory with linear scaling in inverse temperature.

Dynamical mean-field theory and its cluster extensions provide a very useful approach for examining phase transitions in model Hamiltonians and, in combination with electronic structure theory, constitute powerful methods to treat strongly correlated materials. The key advantage to the technique is that, unlike competing real-space methods, the sign problem is well controlled in the Hirsch-Fye (HF) quantum Monte Carlo used as an exact cluster solver. However, an important computational bottleneck remains; the HF method scales as the cube of the inverse temperature, ß . This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant quantum Monte Carlo which scales linearly in ß , with a quadratic term that comes in to play for the number of time slices larger than hundred, and demonstrate that the sign problem is identical to HF.

Pure Mott phases in confined ultracold atomic systems.

We propose a novel scheme for confining atoms to optical lattices by engineering a spatially inhomogeneous hopping matrix element in the Hubbard-model (HM) description, a situation we term off-diagonal confinement (ODC). We show, via an exact numerical solution of the boson HM with ODC, that this scheme possesses distinct advantages over the conventional method of confining atoms using an additional trapping potential, including incompressible Mott phases at commensurate filling and a phase diagram that is similar to the uniform HM. The experimental implementation of ODC will thus allow a more faithful realization of correlated phases in cold-atom experiments.

Parquet approximation for the 4x4 Hubbard cluster.

We present a numerical solution of the parquet approximation, a conserving diagrammatic approach which is self-consistent at both the single-particle and the two-particle levels. The fully irreducible vertex is approximated by the bare interaction thus producing the simplest approximation that one can perform with the set of equations involved in the formalism. The method is applied to the Hubbard model on a half-filled 4x4 cluster. Results are compared to those obtained from determinant quantum Monte Carlo (DQMC), FLuctuation EXchange (FLEX), and self-consistent second-order approximation methods. This comparison shows a satisfactory agreement with DQMC and a significant improvement over the FLEX or the self-consistent second-order approximation.

Relationship between Hirsch-Fye and weak-coupling diagrammatic quantum Monte Carlo methods.

Two weak-coupling continuous time quantum Monte Carlo (CTQMC) methods are shown to be equivalent for Hubbard-type interactions. A relation between these CTQMC methods and the Hirsch-Fye quantum Monte Carlo (HFQMC) method is established, identifying the latter as an approximation within CTQMC and providing a diagrammatic interpretation. Both HFQMC and CTQMC are shown to be equivalent when the number of time slices in HFQMC becomes infinite, implying the same degree of fermion sign problem in this limit.

Quantum critical point at finite doping in the 2D Hubbard model: a dynamical cluster quantum Monte Carlo study.

We explore the Matsubara quasiparticle fraction and the pseudogap of the two-dimensional Hubbard model with the dynamical cluster quantum Monte Carlo method. The character of the quasiparticle fraction changes from non-Fermi-liquid, to marginal Fermi liquid, to Fermi liquid as a function of doping, indicating the presence of a quantum critical point separating non-Fermi-liquid from Fermi-liquid character. Marginal Fermi-liquid character is found at low temperatures at a very narrow range of doping where the single-particle density of states is also symmetric. At higher doping the character of the quasiparticle fraction is seen to cross over from Fermi liquid to marginal Fermi liquid as the temperature increases.

Multi-scale extensions to quantum cluster methods for strongly correlated electron systems.

A numerically implementable multi-scale many-body approach to strongly correlated electron systems is introduced. An extension to quantum cluster methods, it approximates correlations on any given length-scale commensurate with the strength of the correlations on the respective scale. Short length-scales are treated explicitly, long ones are addressed at a dynamical mean-field level and intermediate length-regime correlations are assumed to be weak and are approximated diagrammatically. To illustrate and test this method, we apply it to the one-dimensional Hubbard model. The resulting multi-scale self-energy provides a very good quantitative agreement with substantially more numerically expensive, explicit quantum Monte Carlo calculations.

High-energy kink in the single-particle spectra of the two-dimensional hubbard model.

Employing dynamical cluster quantum Monte Carlo calculations we show that the single-particle spectral weight A(k,omega) of the one-band two-dimensional Hubbard model displays a high-energy kink in the quasiparticle dispersion followed by a steep dispersion of a broad peak similar to recent angle-resolved photoemission spectroscopy results reported for the cuprates. Based on the agreement between the Monte Carlo results and a simple calculation which couples the quasiparticle to spin fluctuations, we conclude that the kink and the broad spectral feature in the Hubbard model spectra is due to scattering with damped high-energy spin fluctuations.

Synergistic polaron formation in the Hubbard-Holstein model at small doping.

We study the effect of dynamical Holstein phonons on the physics of the Hubbard model at small doping using the dynamical cluster approximation on a 2x2 cluster. Nonlocal antiferromagnetic correlations are found to significantly enhance the electron-phonon coupling, resulting in polaron formation for moderate coupling strengths. At finite doping, the electron-phonon coupling is found to strongly enhance the nonlocal spin correlations, indicating a synergistic interplay between the electron-phonon coupling and antiferromagnetic correlations. Although it enhances the pairing interaction, the electron-phonon coupling is found to decrease the superconducting transition temperature, due to the reduction in the quasiparticle fraction.

Pseudogap and antiferromagnetic correlations in the hubbard model.

Using the dynamical cluster approximation and quantum Monte Carlo simulations we calculate the single-particle spectra of the Hubbard model with next-nearest neighbor hopping . In the underdoped region, we find that the pseudogap along the zone diagonal in the electron doped systems is due to long-range antiferromagnetic correlations. The physics in the proximity of (0, pi) is dramatically influenced by t' and determined by the short range correlations. The effect t' of on the low-energy angle-resolved photoemission spectroscopy spectra is weak except close to the zone edge. The short range correlations are sufficient to yield a pseudogap signal in the magnetic susceptibility and produce a concomitant gap in the single-particle spectra near (pi, pi/2), but not necessarily at a location in the proximity of the Fermi surface.

Structure of the pairing interaction in the two-dimensional Hubbard model.

Dynamic cluster Monte Carlo calculations for the doped two-dimensional Hubbard model are used to study the irreducible particle-particle vertex responsible for dx2-y2 pairing in this model. This vertex increases with increasing momentum transfer and decreases when the energy transfer exceeds a scale associated with the Q=(pi, pi) spin susceptibility. Using an exact decomposition of this vertex into a fully irreducible two-fermion vertex and charge and magnetic exchange channels, the dominant part of the effective pairing interaction is found to come from the magnetic, spin S=1 exchange channel.

Systematic study of d-wave superconductivity in the 2D repulsive Hubbard model.

The cluster size dependence of superconductivity in the conventional two-dimensional Hubbard model, commonly believed to describe high-temperature superconductors, is systematically studied using the dynamical cluster approximation and quantum Monte Carlo simulations as a cluster solver. Because of the nonlocality of the d-wave superconducting order parameter, the results on small clusters show large size and geometry effects. In large enough clusters, the results are independent of the cluster size and display a finite temperature instability to d-wave superconductivity.

Kinetic energy driven pairing in cuprate superconductors.

Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the dynamical cluster approximation we study superconductivity in the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional state with partial spin-charge separation, to a superconducting state with quasiparticle excitations.

Zinc impurities in d-wave superconductors.

We study the two-dimensional Hubbard model with nonmagnetic Zn impurities modeled by binary diagonal disorder using quantum Monte Carlo within the dynamical cluster approximation. With increasing Zn content we find a strong suppression of d-wave superconductivity and an enhancement of antiferromagnetic spin correlations. T(c) vanishes linearly with Zn impurity concentration. The spin susceptibility changes from pseudogap to Curie-Weiss-like behavior indicating the existence of free magnetic moments in the Zn doped system. We interpret these results within the resonating-valence-bond picture.

Absence of a Slater transition in the two-dimensional Hubbard model.

We present well-controlled results on the metal-to-insulator transition (MIT) within the paramagnetic solution of the dynamical cluster approximation in the two-dimensional Hubbard model at half filling. In the strong coupling regime, a local picture describes the properties of the model; there is a large charge gap Delta approximately U. In the weak-coupling regime, we find that a symbiosis of short-range antiferromagnetic correlations and moment formation cause a gap to open at finite temperature as in one dimension. Hence, this excludes the mechanism of the MIT proposed by Slater long ago.