Quantum cluster theories

By Thomas A. Maier, M. Jarrell, Thomas Pruschke, M. Hettler. 2004

868 citations recorded by the source corpus.

Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative and are always in the thermodynamic limit. Their quality can be systematically improved, and they provide complementary information to finite size simulations. They have been studied intensively in recent years and are now well established. After a brief historical review, this article comparatively discusses the nature and advantages of these cluster techniques. Applications to common models of correlated electron systems are reviewed.

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

View Paper: https://www.semanticscholar.org/paper/1dd4b493f3517e5f11cc34e8f8fab6e6239ded1c

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Dynamics of non-Markovian open quantum systems (2015, methodology): “…and Kotliar, 1992; Georges et al., 1996; Metzner and Vollhardt, 1989), which is the most widely used numerical method to describe strongly correlated systems in higher than one dimensions (Kotliar et al., 2006; Maier et al., 2005) and is popular also in quantum chemistry (Zgid and Chan, 2011).”
Electronic structure calculations with dynamical mean-field theory (2005, methodology): “…to study some ordered states like d-wave superconductivity which cannot be described by a single-site method Katsnelson and Lichtenstein, 2000; Maier et al., 2000a, 2000b, 2005; Maier, Pruschke, and Jarrell, 2002; Maier, 2003; Macridin et al., 2004, 2005; Maier, Jarrell, Macridin, et al.,…”
Electrodynamics of correlated electron materials (2011, background): “In recent years, cluster extensions of the DMFT were developed (Kotliar et al., 2006; Maier et al., 2005), which treat short range correlations exactly, while the long range correlations are treated on the mean-field level.”
Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach (2016, background): “Hence in the following we review the main results for quantum quenches obtained by means of the Gutzwiller approximation and DMFT.”
TRIQS: A toolbox for research on interacting quantum systems (2015, background): “array ([[1 ,2 ,3] ,[4 ,5 ,6]]) with HDFArchive("data.”
Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model (2020, methodology): “Cellular dynamical mean-field theory (CDMFT) is the real space cluster extension of DMFT [29, 73, 77, 191].”
Pseudogap and Fermi surface topology in the two-dimensional Hubbard model. (2017, methodology): “Let us emphasize the crucial differences that exist between the weak-coupling expression of the self-energy (E5) and both the self-energy that we obtain from DCA at strong coupling, as well as the self-energy obtained from the SU(2) gauge theory.”
Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory (2017, methodology): “DF can be employed as an approximate solver for large clusters occurring in the context of cluster extensions of DMFT (Maier et al., 2005a).”
Continuous-time Monte Carlo methods for quantum impurity models (2010, methodology): “The methods have become very important to the field of correlated electron physics (via the connection to single (Georges et al., 1996) and cluster (Maier et al., 2005a) dynamical mean field theory) and are having an increasing impact on nanoscience.”