arXiv subjects

Emanuel Gull

Publications and source records attributed to Emanuel Gull.

At least 145 records · Page 8Linked to original sources

arXiv2011

Continuous-time Monte Carlo methods for quantum impurity models

Quantum impurity models describe an atom or molecule embedded in a host material with which it can exchange electrons. They are basic to nanoscience as representations of quantum dots and molecular conductors and play an increasingly important role in the theory of "correlated electron" materials as auxiliary problems whose solution gives the "dynamical mean field" approximation to the self energy and local correlation functions. These applications require a method of solution which provides access to both high and low energy scales and is effective for wide classes of physically realistic models. The continuous-time quantum Monte Carlo algorithms reviewed in this article meet this challenge. We present derivations and descriptions of the algorithms in enough detail to allow other workers to write their own implementations, discuss the strengths and weaknesses of the methods, summarize the problems to which the new methods have been successfully applied and outline prospects for future applications.

cond-mat.str-el↗

arXiv2011

Impurity Effects in Highly Frustrated Diamond Lattice Antiferromagnets

We consider the effects of local impurities in highly frustrated diamond lattice antiferromagnets, which exhibit large but non-extensive ground state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an ordered magnetic ground state, and provide a mechanism of degeneracy breaking. The states which are selected can be determined by a "swiss cheese model" analysis, which we demonstrate numerically for a particular impurity model in this case. Moreover, we present criteria for estimating the stability of the resulting ordered phase to a competing frozen (spin glass) one. The results may explain the contrasting finding of frozen and ordered ground states in CoAl2O4 and MnSc2S4, respectively.

cond-mat.str-el↗

arXiv2011

Dynamical mean-field theory for bosons

We discuss the recently developed bosonic dynamical mean-field (B-DMFT) framework, which maps a bosonic lattice model onto the selfconsistent solution of a bosonic impurity model with coupling to a reservoir of normal and condensed bosons. The effective impurity action is derived in several ways: (i) as an approximation to the kinetic energy functional of the lattice problem, (ii) using a cavity approach, and (iii) by using an effective medium approach based on adding a one-loop correction to the selfconsistently defined condensate. To solve the impurity problem, we use a continuous-time Monte Carlo algorithm based on a sampling of a perturbation expansion in the hybridization functions and the condensate wave function. As applications of the formalism we present finite temperature B-DMFT phase diagrams for the bosonic Hubbard model on a 3d cubic and 2d square lattice, the condensate order parameter as a function of chemical potential, critical exponents for the condensate, the approach to the weakly interacting Bose gas regime for weak repulsions, and the kinetic energy as a function of temperature.

cond-mat.str-el↗

arXiv2010

Quenched dynamics in interacting one-dimensional systems: Appearance of current carrying steady states from initial domain wall density profiles

We investigate dynamics arising after an interaction quench in the quantum sine-Gordon model for a one-dimensional system initially prepared in a spatially inhomogeneous domain wall state. We study the time-evolution of the density, current and equal time correlation functions using the truncated Wigner approximation (TWA) to which quantum corrections are added in order to set the limits on its validity. For weak to moderate strengths of the back-scattering interaction, the domain wall spreads out ballistically with the system within the light cone reaching a nonequilibrium steady-state characterized by a net current flow. A steady state current exists for a quench at the exactly solvable Luther-Emery point. The magnitude of the current decreases with increasing strength of the back-scattering interaction. The two-point correlation function of the variable canonically conjugate to the density reaches a spatially oscillating steady state at a wavelength inversely related to the current.

cond-mat.str-el↗

arXiv2010

Bold Line Diagrammatic Monte Carlo Method: General formulation and application to expansion around the Non-Crossing Approximation

We present a general framework for performing "bold-line" diagrammatic Monte Carlo calculations based on using an analytical partial resummation as a starting point for stochastically summing all diagrams. As an example we solve the one orbital Anderson model using the non-crossing approximation as a starting point. We assess the accuracy of the method by using it to solve the equations of single-site dynamical mean field theory. We establish the validity of the starting approximations and show that the bold method provides a very accurate treatment of the Mott-insulating phase.

cond-mat.str-el↗

arXiv2010

Momentum space anisotropy and pseudogaps: a comparative cluster dynamical mean field analysis of the doping-driven metal-insulator transition in the two dimensional Hubbard model

Cluster dynamical mean field calculations based on 2, 4, 8 and 16 site clusters are used to analyze the doping-driven metal-insulator transition in the two dimensional Hubbard model. Comparison of results obtained on different clusters enables a determination of those aspects of the physics that are common to all clusters and permits identification of artifacts associated with particular cluster geometries. A modest particle-hole asymmetry in the underlying band structure is shown to lead to qualitatively different behavior on the hole doped side than on the electron doped side. For particle-hole asymmetry of the sign and magnitude appropriate to high-$T_c$ cuprates, the approach to the insulator from the hole-doping side is found to proceed in two stages from a high-doping region where the properties are those of a Fermi liquid with moderately renormalized parameters and very weak momentum dependence. As doping is reduced the system first enters an intermediate doping regime where the Fermi liquid renormalizations are larger and the electron self energy varies significantly around the Fermi surface and then passes to a small doping regime characterized by a gap in some regions of the Fermi surface but gapless behavior in other regions. On the electron doped side the partially gapped regime does not occur, and the momentum dependence of the electron self energy is less pronounced. Implications for the high-$T_c$ cuprates and for the use of cluster dynamical mean field methods in wider classes of problems are discussed.

cond-mat.str-el↗

arXiv2010

Dynamical mean field solution of the Bose-Hubbard model

We present the effective action and self-consistency equations for the bosonic dynamical mean field (B-DMFT) approximation to the bosonic Hubbard model and show that it provides remarkably accurate phase diagrams and correlation functions. To solve the bosonic dynamical mean field equations we use a continuous-time Monte Carlo method for bosonic impurity models based on a diagrammatic expansion in the hybridization and condensate coupling. This method is readily generalized to bosonic mixtures, spinful bosons, and Bose-Fermi mixtures.

cond-mat.str-el↗

arXiv2010

Physics of the Pseudogap in 8-site Cluster Dynamical Mean Field Theory: photoemission, Raman scattering, in-plane and c-axis conductivity

Cluster dynamical mean field and maximum entropy analytical continuation methods are used to obtain theoretical estimates for the many-body density of states, electron self-energy, in-plane and c-axis optical conductivity and the $B_{1g}$ and $B_{2g}$ Raman scattering spectra of the two dimensional square lattice Hubbard model at intermediate interaction strengths and carrier concentrations near half filling. The calculations are based on an 8-site cluster approximation which gives access to both the zone-diagonal and zone-face portions of the Fermi surface. At low dopings the zone-face regions exhibit a 'pseudogap', a suppression of the many-body density of states for energies near the Fermi surface. The pseudogap magnitude is largest near half filling and decreases smoothly with doping, but as temperature is increased the gap fills in rather than closes. The calculated response functions bear a strong qualitative resemblance to data taken in the pseudogap regime of high-$T_c$ cuprates, strongly suggesting that the intermediate coupling Hubbard model accounts for much of the exotic behavior observed in high-$T_c$ materials.

cond-mat.str-el↗

arXiv2010

Theory of charged impurities in correlated electron materials: Application to muon spectroscopy of high-Tc superconductors

Single-site and cluster dynamical mean-field methods are used to estimate the response of a doped Mott insulator to a charged impurity. The effect of correlations on the Thomas-Fermi screening properties is determined. The charge density, the on-site and near-neighbor spin-spin correlations in the vicinity of the impurity are compared to those far from it. The theory is used to address the question of the effect of the density perturbation induced by the muon charge on the local response functions of a high-temperature superconductor. For reasonable values of the background dielectric constant and basic correlation strength, a muon is shown to lead to an observable perturbation of the local spin dynamics, raising questions about the interpretation of muon-spin-rotation experiments in metallic high-temperature superconductors.

cond-mat.str-el↗

arXiv2010

Optimized broad-histogram simulations for strong first-order phase transitions: Droplet transitions in the large-Q Potts model

The numerical simulation of strongly first-order phase transitions has remained a notoriously difficult problem even for classical systems due to the exponentially suppressed (thermal) equilibration in the vicinity of such a transition. In the absence of efficient update techniques, a common approach to improve equilibration in Monte Carlo simulations is to broaden the sampled statistical ensemble beyond the bimodal distribution of the canonical ensemble. Here we show how a recently developed feedback algorithm can systematically optimize such broad-histogram ensembles and significantly speed up equilibration in comparison with other extended ensemble techniques such as flat-histogram, multicanonical or Wang-Landau sampling. As a prototypical example of a strong first-order transition we simulate the two-dimensional Potts model with up to Q=250 different states on large systems. The optimized histogram develops a distinct multipeak structure, thereby resolving entropic barriers and their associated phase transitions in the phase coexistence region such as droplet nucleation and annihilation or droplet-strip transitions for systems with periodic boundary conditions. We characterize the efficiency of the optimized histogram sampling by measuring round-trip times tau(N,Q) across the phase transition for samples of size N spins. While we find power-law scaling of tau vs. N for small Q \lesssim 50 and N \lesssim 40^2, we observe a crossover to exponential scaling for larger Q. These results demonstrate that despite the ensemble optimization broad-histogram simulations cannot fully eliminate the supercritical slowing down at strongly first-order transitions.

cond-mat.stat-mech↗

arXiv2009

Momentum-sector-selective metal-insulator transition in the eight-site dynamical mean-field approximation to the Hubbard model in two dimensions

We explore the momentum-sector-selective metal insulator transitions recently found in the eight - site dynamical cluster approximation to the two-dimensional Hubbard model. The phase diagram in the space of interaction and second-neighbor hopping is established. The initial transitions from Fermi-liquid like to sector-selective phases are found to be of second order, caused by the continuous opening of an energy gap whereas the other transitions are found to be of first order. In the sector-selective phase the Fermi surface regions which are not gapped are found to have a non-Fermi-liquid self-energy. We demonstrate that the phenomenon is not caused by the Van Hove divergence in the density of states. The sector-selective and insulating phases are characterized by a cluster spin correlation function that is strongly peaked at the commensurate antiferromagnetic wave vector $(π,π)$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.

cond-mat.str-el↗

arXiv2009

Optical conductivity in cluster dynamical mean field theory: formalism and application to high temperature superconductors

The optical conductivity of the one-band Hubbard model is calculated using the 'Dynamical Cluster Approximation' implementation of dynamical mean field theory for parameters appropriate to high temperature copper-oxide superconductors. The calculation includes vertex corrections and the result demonstrates their importance. At densities of one electron per site, an insulating state is found with gap value and above-gap absorption consistent with measurements. As carriers are added the above gap conductivity rapidly weakens and a three component structure emerges, with a low frequency 'Drude' peak, a mid-infrared absorption, and a remnant of the insulating gap. The mid-infrared feature obtained at intermediate dopings is shown to arise from a pseudogap structure in the density of states. On further doping the conductivity evolves to the Drude peak plus weakly frequency dependent tail structure expected for less strongly correlated metals.

cond-mat.str-el↗

arXiv2009

Antiferromagnetism and the gap of a Mott insulator: Results from analytic continuation of the self-energy

Direct analytic continuation of the self energy is used to determine the effect of antiferromagnetic ordering on the spectral function and optical conductivity of a Mott insulator. Comparison of several methods shows that the most robust estimation of the gap value is obtained by use of the real part of the continued self energy in the quasiparticle equation within the single-site dynamical mean field theory of the two dimensional square lattice Hubbard model, where for U slightly greater than the Mott critical value, antiferromagnetism increases the gap by about 80%.

cond-mat.str-el↗

arXiv2009

Two-stage metal-insulator transition in the 2D Hubbard model: momentum selectivity in the 8-site dynamical cluster approximation

Metal-insulator transitions in the paramagnetic phase of the two dimensional square lattice Hubbard model are studied using the dynamical cluster approximation with eight momentum cells. We show that both the interaction-driven and the doping-driven transition are multi-stage and momentum-sector specific, with Fermi liquid metal and fully gapped insulator phases separated by an intermediate phase in which some regions of the Brillouin zone are gapped while others sustain gapless quasiparticles. We argue that this is the coarse-grained version of a gradually shrinking arc or pocket. A pronounced particle-hole asymmetry is found.

cond-mat.str-el↗

arXiv2008

Metal-Insulator phase diagram and orbital selectivity in 3-orbital models with rotationally invariant Hund coupling

A three band model containing the essential physics of transition metal oxides with partially filled t_2g shells is solved in the single-site dynamical mean field approximation, using the full rotationally invariant Slater-Kanamori interactions. We compute the metal-Mott insulator phase diagram in the space of chemical potential and interaction strength, determine the response of the different phases to perturbations which break the orbital symmetry, and establish the regimes in which an orbital selective Mott phase occurs. The results are compared to data on titanates, ruthenates, vanadates and C_60.

cond-mat.str-el↗

arXiv2008

Local Order and the gapped phase of the Hubbard model: a plaquette dynamical mean field investigation

The four-site DCA method of including intersite correlations in the dynamical mean field theory is used to investigate the metal-insulator transition in the Hubbard model. At half filling a gap-opening transition is found to occur as the interaction strength is increased beyond a critical value. The gapped behavior found in the 4-site DCA approximation is shown to be associated with the onset of strong antiferromagnetic and singlet correlations and the transition is found to be potential energy driven. It is thus more accurately described as a Slater phenomenon (induced by strong short ranged order) than as a Mott phenomenon. Doping the gapped phase leads to a non-Fermi-liquid state with a Fermi surface only in the nodal regions and a pseudogap in the antinodal regions at lower dopings $x \lesssim 0.15$ and to a Fermi liquid phase at higher dopings.

cond-mat.str-el↗

arXiv2008

Spin freezing transition and non-Fermi-liquid self-energy in a 3-orbital model

A single-site dynamical mean field study of a three band model with the rotationally invariant interactions appropriate to the t_2g levels of a transition metal oxide reveals a quantum phase transition between a paramagnetic metallic phase and an incoherent metallic phase with frozen moments. The Mott transitions occurring at electron densities n=2,3 per site take place inside the frozen moment phase. The critical line separating the two phases is characterized by a self energy with the frequency dependence Σ(ω)\sim \sqrtω and a broad quantum critical regime. The findings are discussed in the context of the power law observed in the optical conductivity of SrRuO_3.

cond-mat.str-el↗

arXiv2008

Continuous-time auxiliary field Monte Carlo for quantum impurity models

We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization errors, and is particularly useful as impurity solver in large cluster dynamical mean field theory (DMFT) calculations.

cond-mat.str-el↗