Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Bulletin of the American Physical Society

The Continuous Time Quantum Monte Carlo method as a cluster solver in the Dynamical Cluster Approximation

Karlis Mikelsons, Alexandru Macridin, Mark Jarrell, Emanuel Gull, Matthias Troyer, Sebastian Fuchs, Thomas Pruschke

Published Mar 13, 2008• 0 citations
OpenAlex

Related papers

Continuous-time quantum Monte Carlo impurity solvers

Emanuel Gull, Philipp Werner, Sebastian Fuchs +3 more

Computer Physics Communications•Jan 12, 2011•71 citations

Cluster Monte Carlo Method for Quantum Systems

Naoki Kawashima

Springer proceedings in physics•Jan 1, 1997•1 citation

The Dynamical Cluster Approximation with Quantum Monte Carlo Cluster Solvers

Mark Jarrell, Alexandru Macridin, Karlis Mikelsons +4 more

We present a pedagogical discussions of the dynamical mean field (DMFA) and dynamical cluster (DCA) approximations and associated Monte Carlo and entropy‐based methods of Bayesian data analysis. The DMFA and DCA methods are developed as coarse‐graining approximations and the relationship between the cluster and lattice problems are detailed. The Hirsch‐Fye and continuous time Quantum Monte Carlo (QMC) algorithms are used to solve the cluster problem. The algorithms are discussed, together with methods for efficient measurements and the modifications required by the self‐consistency of the DMFA/DCA. Then, several principles of Bayesian data analysis are presented. When coupled with information theory, this analysis produces a precise and systematic way to analytically continue Matsubara‐time QMC results to real frequencies. We show how to use Bayesian inference to qualify the solution of the continuation and optimize the inputs. Besides developing the Bayesian formalism, we also present a detailed description of the data qualification, sketch an efficient algorithm to solve for the optimal spectra, give cautionary notes where appropriate, and present two detailed case studies to demonstrate the method.

AIP conference proceedings•Jan 1, 2008•5 citations

Semiclassical approximation solved by Monte Carlo integration as an efficient impurity solver for dynamical mean field theory and its cluster extensions

Hunpyo Lee, Yu‐Zhong Zhang, Hoonkyung Lee +3 more

We propose that a combination of the semiclassical approximation with Monte Carlo simulations can be an efficient and reliable impurity solver for dynamical mean field theory equations and their cluster extensions with large cluster sizes. In order to show the reliability of the method, we consider two test cases: (i) the single-band Hubbard model within the dynamical cluster approximation with four- and eight-site clusters and (ii) the anisotropic two-orbital Hubbard model with orbitals of different bandwidth within the single-site dynamical mean field theory. We compare the critical interaction ${U}_{c}/t$ with those obtained from solving the dynamical mean field equations with the continuous-time and Hirsch-Fye quantum Monte Carlo approaches. In both test cases we observe reasonable values of the metal-insulator critical interaction strength ${U}_{c}/t$ and the nature of Mott physics in the self-energy behavior. While some details of the spectral functions cannot be captured by the semiclassical approximation due to the freezing of dynamical fluctuations, the main features are reproduced by the approach.

arXiv:1303.6813•Physical Review B•Oct 18, 2013•5 citations

Fermionic and Continuous Time Quantum Monte Carlo

Emanuel Gull, Matthias Troyer

Springer series in solid-state sciences•Jan 1, 2013•1 citation

Accessing thermodynamics from dynamical cluster-embedding approaches

Gang Li, Werner R. Hanke, Alexey N. Rubtsov +2 more

Dynamical quantum-cluster approaches, such as different cluster extensions of the dynamical mean-field theory (cluster DMFT) or the variational cluster approximation (VCA), combined with efficient cluster solvers, such as the quantum Monte Carlo (QMC) method, provide controlled approximations of the single-particle Green's function for lattice models of strongly correlated electrons. To access the thermodynamics, however, a thermodynamical potential is needed. We present an efficient numerical algorithm to compute the grand potential within cluster-embedding approaches that are based on novel continuous-time QMC schemes. It is shown that the numerically exact cluster grand potential can be obtained from a quantum Wang-Landau technique to reweight the coefficients in the expansion of the partition function. The lattice contributions to the grand potential are computed by a proper infinite summation over Matsubara frequencies. A proof of principle is given by applying the VCA to antiferromagnetic (short-range) order in the two-dimensional Hubbard model at finite temperatures.

arXiv:0908.0844•Physical Review B•Nov 30, 2009•12 citations
We present a pedagogical discussions of the dynamical mean field (DMFA) and dynamical cluster (DCA) approximations and associated Monte Carlo and entropy‐based methods of Bayesian data analysis. The DMFA and DCA methods are developed as coarse‐graining approximations and the relationship between the cluster and lattice problems are detailed. The Hirsch‐Fye and continuous time Quantum Monte Carlo (QMC) algorithms are used to solve the cluster problem. The algorithms are discussed, together with methods for efficient measurements and the modifications required by the self‐consistency of the DMFA/DCA. Then, several principles of Bayesian data analysis are presented. When coupled with information theory, this analysis produces a precise and systematic way to analytically continue Matsubara‐time QMC results to real frequencies. We show how to use Bayesian inference to qualify the solution of the continuation and optimize the inputs. Besides developing the Bayesian formalism, we also present a detailed description of the data qualification, sketch an efficient algorithm to solve for the optimal spectra, give cautionary notes where appropriate, and present two detailed case studies to demonstrate the method.
We propose that a combination of the semiclassical approximation with Monte Carlo simulations can be an efficient and reliable impurity solver for dynamical mean field theory equations and their cluster extensions with large cluster sizes. In order to show the reliability of the method, we consider two test cases: (i) the single-band Hubbard model within the dynamical cluster approximation with four- and eight-site clusters and (ii) the anisotropic two-orbital Hubbard model with orbitals of different bandwidth within the single-site dynamical mean field theory. We compare the critical interaction Uc/t{U}_{c}/tUc​/t with those obtained from solving the dynamical mean field equations with the continuous-time and Hirsch-Fye quantum Monte Carlo approaches. In both test cases we observe reasonable values of the metal-insulator critical interaction strength Uc/t{U}_{c}/tUc​/t and the nature of Mott physics in the self-energy behavior. While some details of the spectral functions cannot be captured by the semiclassical approximation due to the freezing of dynamical fluctuations, the main features are reproduced by the approach.
Dynamical quantum-cluster approaches, such as different cluster extensions of the dynamical mean-field theory (cluster DMFT) or the variational cluster approximation (VCA), combined with efficient cluster solvers, such as the quantum Monte Carlo (QMC) method, provide controlled approximations of the single-particle Green's function for lattice models of strongly correlated electrons. To access the thermodynamics, however, a thermodynamical potential is needed. We present an efficient numerical algorithm to compute the grand potential within cluster-embedding approaches that are based on novel continuous-time QMC schemes. It is shown that the numerically exact cluster grand potential can be obtained from a quantum Wang-Landau technique to reweight the coefficients in the expansion of the partition function. The lattice contributions to the grand potential are computed by a proper infinite summation over Matsubara frequencies. A proof of principle is given by applying the VCA to antiferromagnetic (short-range) order in the two-dimensional Hubbard model at finite temperatures.