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

Dynamical Mean Field Theory Cluster Solver with Linear Scaling in Inverse Temperature

Ehsan Khatami, C. R. Lee, Zhaojun Bai, Richard T. Scalettar, Mark Jarrell

Published Apr 7, 2009• 3 citations
OpenAlex

Related papers

Quasi-continuous-time impurity solver for the cluster dynamical mean-field theory with linear scaling in the inverse temperature

D. Rost, Fakher F. Assaad, Nils Bl umer

Bulletin of the American Physical Society•Mar 5, 2015•0 citations

A linear in $\beta$ solver for Cluster Dynamical Mean Field Theory

Ehsan Khatami, Mark Jarrell, Che–Rung Lee +1 more

Bulletin of the American Physical Society•Mar 19, 2009•0 citations

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

Ehsan Khatami, C. R. Lee, Zhaojun Bai +2 more

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, β . This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant quantum Monte Carlo which scales linearly in β , 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.

arXiv:0904.1239•Physical Review E•May 12, 2010•18 citations

Quasi-continuous-time impurity solver for the dynamical mean-field theory with linear scaling in the inverse temperature

D. Rost, Fakher F. Assaad, Nils Blümer

We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.

arXiv:1303.2004•Physical Review E•May 29, 2013•16 citations

Cluster Dynamical Mean Field Theory

David Sénéchal

Springer series in solid-state sciences•Aug 9, 2011•22 citations

Dynamical Mean Field Theory

Yoshio Kuramoto

Lecture notes in physics•Jan 1, 2020•0 citations
A linear in β\betaβ solver for Cluster Dynamical Mean Field Theory
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, β . This often makes simulations at low temperatures extremely challenging. We present here a method based on determinant quantum Monte Carlo which scales linearly in β , 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.
We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.