# Continuous-time Monte Carlo methods for quantum impurity models

@article{Gull2010ContinuoustimeMC, title={Continuous-time Monte Carlo methods for quantum impurity models}, author={Emanuel Gull and Andrew J. Millis and Alexander I. Lichtenstein and Alexey N. Rubtsov and Matthias Troyer and Philipp Werner}, journal={Reviews of Modern Physics}, year={2010}, volume={83}, pages={349-404} }

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…

## 804 Citations

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Abstract
The solution of an auxiliary quantum impurity system is the computationally expensive step in dynamical mean field theory simulations of lattice models and materials. In this review, we…

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Dynamical mean-field theory (DMFT) is one of the most widely-used methods to treat accurately electron correlation effects in ab-initio real material calculations. Many modern large-scale…

### Improved Hubbard-I approximation impurity solver for quantum impurity models

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A fast impurity solver based on the combination of Hubbard-I approximation and hybridization expansion continuous-time quantum Monte Carlo algorithm which is suggested that is very suitable to solve the multi-orbital quantum impurity models efficiently and can be used to study more realistic systems with magnetic long-range order in the future.

### : An open source continuous-time quantum Monte Carlo impurity solver toolkit

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### Diagrammatic Monte Carlo method for impurity models with general interactions and hybridizations

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The diagrammatic Monte Carlo method is presented, which uses a recursive determinant scheme to sample diagrams for the scattering amplitude and is ideal for quantum impurity problems with a large number of orbitals but only moderate correlations.

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- 2014

A nonperturbative quantum impurity solver is proposed based on a formally exact hierarchical equations of motion (HEOM) formalism for open quantum systems. It leads to quantitatively accurate…

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In low-temperature high-density plasmas quantum effects of the electrons are becoming increasingly important. This requires the development of new theoretical and computational tools. Quantum Monte…

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The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications…

### Numerical renormalization group

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A quantum impurity is a point-like object with local degrees of freedom, such as spin and orbital angular momentum, that interacts with an environment (continuum of states) in such a way that the…

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