The Dynamical Cluster Approximation with Quantum Monte Carlo Cluster Solvers

Jarrell, Mark; Macridin, Alexandru; Mikelsons, Karlis; Doluweera, D. G. S. P.; Gubernatis, J. E.; Avella, Adolfo; Mancini, Ferdinando

doi:10.1063/1.2940445

Cited by 5 publications

(7 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The technical aspects of the approach and its applications to the analytic continuation of imaginary-time data have been discussed in a numerous publications, such as Refs. [21][22][23][24][25].…”

Section: A Formulation Of the Problemmentioning

confidence: 99%

Extracting spectral properties from Keldysh Green functions

et al. 2013

View full text Add to dashboard Cite

We investigate the possibility to assist the numerically ill-posed calculation of spectral properties of interacting quantum systems in thermal equilibrium by extending the imaginary-time simulation to a finite SchwingerKeldysh contour. The effect of this extension is tested within the standard maximum entropy approach to analytic continuation. We find that the inclusion of real-time data improves the resolution of structures at high energy, while the imaginary-time data are needed to correctly reproduce low-frequency features such as quasiparticle peaks. As a nonequilibrium application, we consider the calculation of time-dependent spectral functions from retarded Green function data on a finite time interval, and compare the maximum entropy approach to direct Fourier transformation and a method based on Padé approximants.

show abstract

Section: A Formulation Of the Problemmentioning

confidence: 99%

Extracting spectral properties from Keldysh Green functions

et al. 2013

View full text Add to dashboard Cite

show abstract

“…Additionally, it is well-known that the resolution of low-temperature features with the MaxEnt method requires a careful Bayesian analysis based on higher-temperature data, i.e. an "annealing procedure", involving a sequence of QMC plus MaxEnt runs for a reasonably fine temperature grid 27,28 .…”

Section: E Numerical Implementation Of Q Rϑmentioning

confidence: 99%

“…A common way to deal with this problem is the so-called "annealing procedure". 28,29 Here, a fine temperature grid is imposed in order to freeze out low-energy features step by step. The procedure starts with a featureless default model at very high temperatures.…”

Section: Approaching Lower Temperaturesmentioning

confidence: 99%

See 1 more Smart Citation

Imaginary-time quantum many-body theory out of equilibrium. II. Analytic continuation of dynamic observables and transport properties

et al. 2013

View full text Add to dashboard Cite

Within 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 non-equilibrium and current-voltage characteristics for different values of the dot charging energy.

show abstract

“…The complexification of the voltage bias, however, introduces a formidable new problem in the form of an analytical continuation with respect to the voltage on top of the already challenging analytic continuation from Matsubara frequencies to real frequencies. In a recent preprint [19] we applied Continuous-Time Quantum Monte Carlo [20][21][22] in order to obtain high-quality data and proposed a scheme for analytical continuation using a Maximum Entropy Method [23,24]. For the latter purpose, a linear integral equation was derived.…”

Section: Introductionmentioning

confidence: 99%

CT-QMC and Maximum Entropy Approach to a Scattering-States Formulation of Strongly Correlated Steady-State Transport

Dirks

Werner

Jarrell

et al. 2011

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

Abstract. In a recent work [17] Han and Heary introduced a formalism approaching steadystate quantum transport through mesoscopic structures which maps the non-equilibrium problem onto a family of auxiliary equilibrium quantum impurity systems by introducing imaginary voltages. We apply continuous-time quantum Monte-Carlo solvers to obtain precise and unbiased imaginary-time data for these auxiliary models. Physical observables are obtained by an analytical continuation in both Matsubara frequency and complexified voltage using a Maximum Entropy Method (MEM). The MEM is introduced by means of a kernel function compatible with the analytical structure of the theory. While it remains a yet challenging task to obtain reliable spectral functions, this unbiased procedure seems to indicate that the formalism yields results which are compatible with those of other methods. IntroductionCalculating steady-state transport properties of open quantum systems is a challenging and unsolved problem. It has been approached by perturbative methods [1][2][3], the time-dependent density matrix renormalization group (t-DMRG) [4,5], real-time quantum Monte Carlo (RT-QMC) [6][7][8][9], numerical renormalization group (NRG) [10], and the functional renormalization group (fRG) [11][12][13][14][15][16]. However, none of the methods developed so far is able to give a complete and reliable description of the physical properties in all parameter regimes. More importantly, the most interesting regime, where all relevant energy scales -voltage, temperature, magnetic field, etc. -are of the same order as the low-energy scale of the Anderson Impurity Model, is usually not accessible. Therefore, the development of new or improved simulation approaches is a worthwhile and important task.Recently, a new and rather unconventional approach to calculate the steady-state transport through interacting quantum dots or similar structures was proposed by Han and Heary [17]. Their formalism, which is based on Hershfield's density operator [18], maps the non-equilibrium steady-state of the interacting model onto an infinite set of auxiliary equilibrium systems, each characterized by some complex voltage. The complexification of the voltage bias, however, introduces a formidable new problem in the form of an analytical continuation with respect to

show abstract

The Dynamical Cluster Approximation with Quantum Monte Carlo Cluster Solvers

Cited by 5 publications

References 40 publications

Extracting spectral properties from Keldysh Green functions

Extracting spectral properties from Keldysh Green functions

Imaginary-time quantum many-body theory out of equilibrium. II. Analytic continuation of dynamic observables and transport properties

CT-QMC and Maximum Entropy Approach to a Scattering-States Formulation of Strongly Correlated Steady-State Transport

Contact Info

Product

Resources

About