Continuous-time Monte Carlo methods for quantum impurity models

By Emanuel Gull, A. Millis, A. Lichtenstein, A. Rubtsov, Matthias Troyer, Philipp Werner. 2010

1,064 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/08904a4060a9468b086f5ce1b504009204386a73

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Rubtsov
2. Gian-Marco Rignanese
3. N. Tsuji
4. M. Kollar
5. Martin Eckstein
6. H. Aoki
7. T. Oka
8. Philipp Werner

In Condensed Matter Physics

1. A. Rubtsov
2. Philipp Werner
3. Hartmut Hafermann
4. Olivier Parcollet
5. T. Oka
6. M. Kollar
7. H. Aoki
8. N. Tsuji

Citations in the corpus

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory (2017, methodology): “It also fostered the development of new impurity solvers (Bulla et al., 2008; Gull et al., 2011b).”
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model (2020, methodology): “The auxiliary impurity models were solved using a state-of-the-art continuous time quantum Monte Carlo impurity solver in its interaction expansion (CT-INT [165, 181, 182]) implemented in the TRIQS framework [183].”
• Nonequilibrium dynamical mean-field theory and its applications (2013, background): “(143) can be obtained by a fast-update algorithm with a computational cost ofO(n2) (Gull et al., 2011a).”
• TRIQS: A toolbox for research on interacting quantum systems (2015, methodology): “For optimal efficiency within a Monte Carlo framework, the modifications to the matrices can be done in two steps: a first step which only returns the determinant ratio between the matrix before (M) and after the modification (M ′), i.e. ξ = detM ′/ detM (which is generally used in the acceptance ra”
• Dynamics of non-Markovian open quantum systems (2015, methodology): “These diagrammatic Monte Carlo algorithms are the basis for the so-called continuous time quantum Monte Carlo methods, discussed in detail by Gull et al. (2011).”
• Recent developments in the ABINIT software package (2016, methodology): “The non diagonal hybridization and coupling to the exact rotationally invariant interaction [103] is not available in version 7.”
• Band geometry, Berry curvature and superfluid weight (2016, methodology): “8) we use a continuous-time interaction-expansion (CT-INT) impurity solver [66, 67] and for larger U we resort to exact diagonalization [64, 68] in solving the impurity problem.”
• A substantial hybridization between correlated Ni-d orbital and itinerant electrons in infinite-layer nickelates (2019, methodology): “DMFT maps the interacting lattice Hamiltonian onto an auxiliary impurity problem which is solved using the continuous-time quantum Monte Carlo algorithm based on hybridization expansion [64, 65].”