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Emanuel Gull

Publications and source records attributed to Emanuel Gull.

At least 91 records · Page 5Linked to original sources
arXiv2019

Lead Geometry and Transport Statistics in Molecular Junctions

We present a numerically exact study of charge transport and its fluctuations through a molecular junction driven out of equilibrium by a bias voltage, using the Inchworm quantum Monte Carlo (iQMC) method. After showing how the technique can be used to address any lead geometry, we concentrate on one dimensional chains as an example. The finite bandwidth of the leads is shown to affect transport properties in ways that cannot be fully captured by quantum master equations: in particular, we reveal an interaction-induced broadening of transport channels that is visible at all voltages, and show how fluctuations of the current are a more sensitive probe of this effect than the mean current.

physics.chem-ph↗
arXiv2019

Magnetic Susceptibility and Simulated Neutron Signal in the 2D Hubbard Model

We compute dynamic spin susceptibilities in the two-dimensional Hubbard model using the method of Dual Fermions and provide comparison to lattice Monte Carlo and cluster dynamical mean field theory. We examine the energy dispersion identified by peaks in ${\rm Im}χ(ω,q)$ which define spin modes and compare the exchange scale and magnon dispersion to neutron experiments on the parent La$_2$CuO$_4$ cuprate. We present the evolution of the spin excitations as a function of Hubbard interaction strengths and doping and explore the particle-hole asymmetry of the spin excitations. We also study the correlation lengths and the spin excitation dispersion peak structure and find a `Y'-shaped dispersion similar to neutron results on doped HgBa$_2$CuO$_{4+δ}$.

cond-mat.str-el↗
arXiv2019

Charge order and antiferromagnetism in the extended Hubbard model

We study the extended Hubbard model on a two-dimensional half-filled square lattice using the dynamical cluster approximation. We present results on the phase boundaries between the paramagnetic metallic (normal) state and the insulating antiferromagnetic state, as well as between the antiferromagnetic and charge order states. We find hysteresis along the antiferromagnet/charge order and normal/charge order phase boundaries (at larger values of the on-site interaction), indicating first order phase transitions. We show that nearest neighbor interactions lower the critical temperature for the antiferromagnetic phase. We also present results for the effect of nearest neighbor interactions on the antiferromagnetic phase boundary and for the evolution of spectral functions and energetics across the phase transitions.

cond-mat.str-el↗
arXiv2018

Updated Core Libraries of the ALPS Project

The open source ALPS (Algorithms and Libraries for Physics Simulations) project provides a collection of physics libraries and applications, with a focus on simulations of lattice models and strongly correlated electron systems. The libraries provide a convenient set of well-documented and reusable components for developing condensed matter physics simulation codes, and the applications strive to make commonly used and proven computational algorithms available to a non-expert community. In this paper we present an update of the core ALPS libraries. We present in particular new Monte Carlo libraries and new Green's function libraries.

physics.comp-ph↗
arXiv2018

Chebyshev polynomial representation of imaginary time response functions

Problems of finite-temperature quantum statistical mechanics can be formulated in terms of imaginary (Euclidean) -time Green's functions and self-energies. In the context of realistic Hamiltonians, the large energy scale of the Hamiltonian (as compared to temperature) necessitates a very precise representation of these functions. In this paper, we explore the representation of Green's functions and self-energies in terms of a series of Chebyshev polynomials. We show that many operations, including convolutions, Fourier transforms, and the solution of the Dyson equation, can straightforwardly be expressed in terms of the series expansion coefficients. We then compare the accuracy of the Chebyshev representation for realistic systems with the uniform-power grid representation, which is most commonly used in this context.

cond-mat.stat-mech↗
arXiv2018

Inclusion-Exclusion Principle for Many-Body Diagrammatics

Recent successes in Monte Carlo methods for simulating fermionic quantum impurity models have been based on diagrammatic resummation techniques, but are restricted by the need to sum over factorially large classes of diagrams individually. We present a fast algorithm for summing over the diagrams appearing in Inchworm hybridization expansions. The method relies on the inclusion-exclusion principle to reduce the scaling from factorial to exponential. We analyze the growth rate and compare with related algorithms for expansions in the many-body interaction. An implementation demonstrates that for a simulation of a concrete physical model at reasonable parameters and accuracy, our algorithm not only scales better asymptotically, but also provides performance gains of approximately two orders of magnitude in practice over the previous state-of-the-art.

cond-mat.str-el↗
arXiv2018

Overcomplete compact representation of two-particle Green's functions

Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large computation time and massive memory consumption. We derive a general expansion formula for the two-particle Green's functions in terms of an overcomplete representation based on the recently proposed "intermediate representation" basis. The expansion formula is obtained by decomposing the spectral representation of the two-particle Green's function. We demonstrate that the expansion coefficients decay exponentially, while all high-frequency and long-tail structures in the Matsubara-frequency domain are retained. This representation therefore enables efficient treatment of two-particle quantities and opens a route to the application of modern many-body theories to realistic strongly correlated electron systems.

cond-mat.str-el↗
arXiv2018

Numerically exact full counting statistics of the nonequilibrium Anderson impurity model

The time dependent full counting statistics of charge transport through an interacting quantum junction is evaluated from its generating function, controllably computed with the inchworm Monte Carlo method. Exact noninteracting results are reproduced; then, we continue to explore the effect of electron--electron interactions on the time-dependent charge cumulants, first-passage time distributions and $n$-electron transfer distributions. We observe a crossover in the noise from Coulomb blockade- to Kondo-dominated physics as the temperature is decreased. In addition, we uncover long-tailed spin distributions in the Kondo regime and analyze queuing behavior caused by correlations between single electron transfer events.

cond-mat.mes-hall↗
arXiv2018

Charge ordering and non-local correlations in the doped extended Hubbard model

We study the extended Hubbard model away from half-filling on a two-dimensional square lattice using cluster dynamical mean field theory on clusters of size $8$. We show that the model exhibits metallic, compressible charge ordered, and insulating charge ordered phases. We determine the location of the charge ordering phase transition line at finite temperature and the properties of the phases as a function of doping, temperature, local interaction, and nearest neighbor interaction. An analysis of the energetics of the charge order transition shows that the charge ordering transition mainly results in a rearrangement of local and non-local potential energy. We show the doping evolution of the spectral function from the isotropic metal via a charge ordered metal to a charge ordered insulator with a big gap, and study finite size effects of the approximation.

cond-mat.str-el↗
arXiv2018

Hypothesis testing of scientific Monte Carlo calculations

The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and programming bugs. However, the testing paradigms developed for deterministic algorithms have proven to be ill suited for stochastic algorithms. In this paper we demonstrate explicitly how the technique of statistical hypothesis testing, which is in wide use in other fields of science, can be used to devise automatic and reliable tests for Monte Carlo methods, and we show that these tests are able to detect some of the common problems encountered in stochastic scientific simulations. We argue that hypothesis testing should become part of the standard testing toolkit for scientific simulations.

physics.comp-ph↗
arXiv2017

Momentum-Space Cluster Dual Fermion Method

Recent years have seen the development of two types of non-local extensions to the single-site dynamical mean field theory. On one hand, cluster approximations, such as the dynamical cluster approximation, recover short-range momentum-dependent correlations non-perturbatively. On the other hand, diagrammatic extensions, such as the dual fermion theory, recover long ranged corrections perturbatively. The correct treatment of both strong short-ranged and weak long-ranged correlations within the same framework is therefore expected to lead to a quick convergence of results, and offers the potential of obtaining smooth self-energies in non-perturbative regimes of phase space. In this paper, we present an exact cluster dual fermion method based on an expansion around the dynamical cluster approximation. Unlike previous formulations, our method does not employ a coarse graining approximation to the interaction, which we show to be the leading source of error at high temperature, and converges to the exact result independent of the size of the underlying cluster. We illustrate the power of the method with results for the second-order cluster dual fermion approximation to the single-particle self-energies and double occupancies.

cond-mat.str-el↗
arXiv2017

Implementation of the Bin Hierarchy Method for restoring a smooth function from a sampled histogram

We present $\texttt{BHM}$, a tool for restoring a smooth function from a sampled histogram using the bin hierarchy method. The theoretical background of the method is presented in [arXiv:1707.07625]. The code automatically generates a smooth polynomial spline with the minimal acceptable number of knots from the input data. It works universally for any sufficiently regular shaped distribution and any level of data quality, requiring almost no external parameter specification. It is particularly useful for large-scale numerical data analysis. This paper explains the details of the implementation and the use of the program.

stat.OT↗
arXiv2017

Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bondlength, with a confidence bound given on all uncertainties.

physics.comp-ph↗
arXiv2017

Testing self-energy embedding theory in combination with GW

We present a theoretical framework and implementation details for self-energy embedding theory (SEET) with the GW approximation for the treatment of weakly correlated degrees of freedom and configuration interactions solver for handing the strongly correlated degrees. On a series of molecular examples, for which the exact results are known within a given basis, we demonstrate that SEET(CI/GW) is a systematically improvable and well controlled method capable of giving accurate results and well behaved causal self-energies and Green's functions. We compare the theoretical framework of SEET(CI/GW) to that of GW+DMFT and comment on differences between these to approaches that aim to treat both strongly and weakly correlated simultaneously.

cond-mat.str-el↗
arXiv2017

Quantum Monte Carlo solution of the dynamical mean field equations in real time

We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real-time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo methods have now reached a state where they can be used as dynamical mean field impurity solvers and the dynamical sign problem can be overcome. As non-equilibrium problems can be simulated at the same cost, we envisage the main use of these methods as dynamical mean field solvers for time-dependent problems far from equilibrium.

cond-mat.str-el↗
arXiv2017

Finite temperature quantum embedding theories for correlated systems

The cost of the exact solution of the many-electron problem is believed to be exponential in the number of degrees of freedom, necessitating approximations that are controlled and accurate but numerically tractable. In this paper, we show that one of these approximations, the self-energy embedding theory (SEET), is derivable from a universal functional and therefore implicitly satisfies conservation laws and thermodynamic consistency. We also show how other approximations, such as the dynamical mean field theory (DMFT) and its combinations with many-body perturbation theory, can be understood as a special case of SEET and discuss how the additional freedom present in SEET can be used to obtain systematic convergence of results.

cond-mat.str-el↗