Continuous-time Monte Carlo methods for quantum impurity models

Abstract

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.

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• Electronic correlations, magnetism and Hund's rule coupling in the ruthenium perovskites SrRuO${}_3$ and CaRuO${}_3$
• Computing total energies in complex materials using charge self-consistent DFT+DMFT
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• Non-Drude universal scaling laws for the optical response of local Fermi liquids
• Systematically improvable multi-scale solver for correlated electron systems
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• Chebyshev expansion for Impurity Models using Matrix Product States
• Bad-metal behavior reveals Mott quantum criticality in doped Hubbard models
• Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
• Extended dynamical mean-field study of the Hubbard model with long range interactions
• Time-Reversal-Invariant Hofstadter-Hubbard Model with Ultracold Fermions
• Energetics of superconductivity in the two dimensional Hubbard model
• Non-perturbative stochastic method for driven spin-boson model
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• $i$QIST: An open source continuous-time quantum Monte Carlo impurity solver toolkit
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• Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance
• Metal-Insulator Transition and Lattice Instability of Paramagnetic V2O3
• c-axis resistivity, pseudogap, superconductivity and Widom line in doped Mott insulators
• First-Order Insulator-to-Metal Mott Transition in the Paramagnetic 3D System GaTa4Se8
• Orbital Polarization in Strained LaNiO${}_3$: Structural Distortions and Correlation Effects
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• Towards a full ab initio theory of strong electronic correlations in nanoscale devices
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• A route to room temperature ferromagnetic ultrathin SrRuO${}_3$ films
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