Quantum Impurity Models as Reference Systems for Strongly Correlated Materials: The Road from the Kondo Impurity Model to First Principles Electronic Structure Calculations with Dynamical Mean-Field Theory

2005 ◽  
Vol 74 (1) ◽  
pp. 147-154 ◽  
Author(s):  
Gabriel Kotliar
Keyword(s):  
First Principles ◽  
Mean Field Theory ◽  
Mean Field ◽  
Strongly Correlated ◽  
Strongly Correlated Materials ◽  
The Road ◽  
Impurity Model ◽  
Quantum Impurity ◽  
Impurity Models ◽  
Structure Calculations

scholarly journals EQUATION-OF-MOTION APPROACH TO DYNAMICAL MEAN FIELD THEORY

2006 ◽  
Vol 20 (25) ◽  
pp. 1629-1636 ◽  
Author(s):  
JIAN-XIN ZHU ◽  
R. C. ALBERS ◽  
J. M. WILLS
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Bethe Lattice ◽  
Equation Of Motion ◽  
Spectral Weight ◽  
Dynamical Mean Field Theory ◽  
Strongly Correlated ◽  
Strongly Correlated Materials ◽  
Weight Transfer

We propose using an equation-of-motion approach as an impurity solver for dynamical mean field theory. As an illustration of this technique, we consider a finite-U Hubbard model defined on the Bethe lattice with infinite connectivity at arbitrary filling. Depending on the filling, the spectra that is obtained exhibits a quasiparticle peak, and lower and upper Hubbard bands as typical features of strongly correlated materials. The results are also compared and in good agreement with exact diagonalization. We also find a different picture of the spectral weight transfer than the iterative perturbation theory.

scholarly journals Maximally Localized Dynamical Quantum Embedding for Solving Many-Body Correlated Systems

2020 ◽  
Author(s):  
Carla Lupo ◽  
Wai Hei Terence Tze ◽  
Francois Jamet ◽  
Ivan Rungger ◽  
Cedric Weber
Keyword(s):  
Degrees Of Freedom ◽  
Mean Field Theory ◽  
Mean Field ◽  
Many Body ◽  
Correlated Systems ◽  
Impurity Model ◽  
Quantum Impurity ◽  
Diagonalization Method ◽  
Large Benefit ◽  
Exact Diagonalization Method

Abstract We present a quantum embedding methodology to resolve the Anderson impurity model in the context of dynamical mean-field theory, based on an extended exact diagonalization method. Our method provides a maximally localized quantum impurity model, where the non-local components of the correlation potential remain minimal. This comes at a large benefit, as the environment used in the quantum embedding approach is described by propagating correlated electrons and hence offers an exponentially increasing number of degrees of freedom for the embedding mapping, in contrast to traditional free-electron representation where the scaling is linear. We report that quantum impurity models with as few as 3 bath sites can reproduce both the Mott transition and the Kondo physics, thus opening a more accessible route to the description of time-dependent phenomena. Finally, we obtain excellent agreement for dynamical magnetic susceptibilities, poising this approach as a candidate to describe 2-particle excitations such as excitons in correlated systems. We expect that our approach will be highly beneficial for the implementation of embedding algorithms on quantum computers, as it allows for a fine description of the correlation in materials with a reduced number of required qubits.

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