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Dynamical Mean-Field Theory (DMFT) is a powerful theoretical framework for analyzing systems with many interacting degrees of freedom. This tutorial provides an accessible introduction to DMFT. We begin with a linear model where the DMFT…

Disordered Systems and Neural Networks · Physics 2025-07-23 Emmy Blumenthal

We explore the use of exact diagonalization methods for solving the self consistent equations of the cellular dynamical mean field theory (CDMFT) for the one dimensional regular and extended Hubbard models. We investigate the nature of the…

Strongly Correlated Electrons · Physics 2007-05-23 C. J. Bolech , S. S. Kancharla , G. Kotliar

Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…

Computational Engineering, Finance, and Science · Computer Science 2019-08-27 Sergio Lucarini , Javier Segurado

We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity-solver of the Dynamical Mean Field Theory (DMFT). This…

Strongly Correlated Electrons · Physics 2017-11-27 Y. Núñez Fernández , K. Hallberg

A new numerical method for the solution of the Dynamical Mean Field Theory's self-consistent equations is introduced. The method uses the Density Matrix Renormalization Group technique to solve the associated impurity problem. The new…

Strongly Correlated Electrons · Physics 2016-08-31 Daniel J. Garcia , Karen Hallberg , Marcelo J. Rozenberg

The dynamical mean field theory (DMFT) has become a standard technique for the study of strongly correlated models and materials overcoming some of the limitations of density functional approaches based on local approximations. An important…

Strongly Correlated Electrons · Physics 2015-10-28 K. Hallberg , D. J. García , Pablo S. Cornaglia , Jorge I. Facio , Y. Núñez-Fernández

We apply a recently introduced hybridization-flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how…

Strongly Correlated Electrons · Physics 2013-11-21 Michael Kinza , Carsten Honerkamp

We address the steady-state behavior of a system consisting of several correlated monoatomic layers sandwiched between two metallic leads under the influence of a bias voltage. In particular, we investigate the effect of the local Hubbard…

Strongly Correlated Electrons · Physics 2018-08-14 Irakli Titvinidze , Max E. Sorantin , Antonius Dorda , Wolfgang von der Linden , Enrico Arrigoni

The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on conservation of the adiabatic invariant, magnetic moment.…

Plasma Physics · Physics 2019-05-30 Anatoly Neishtadt , Anton Artemyev

We extend a previously proposed rotation and truncation scheme to optimize quantum Anderson impurity calculations with exact diagonalization [PRB 90, 085102 (2014)] to density-matrix renormalization group (DMRG) calculations. The method…

Strongly Correlated Electrons · Physics 2019-10-02 Y. Lu , X. Cao , P. Hansmann , M. W. Haverkort

We propose a method for estimating smooth real-frequency self-energy in the dynamical mean-field theory with the finite-temperature exact diagonalization (DMFT-ED). One of the benefits of DMFT-ED calculations is that one can obtain…

Strongly Correlated Electrons · Physics 2019-06-10 Yuki Nagai , Hiroshi Shinaoka

We introduce a nested optimization procedure using semi-definite relaxation for the fitting step in Hamiltonian-based cluster dynamical mean-field theory (DMFT) methodologies. We show that the proposed method is more efficient and flexible…

Strongly Correlated Electrons · Physics 2020-01-31 Carlos Mejuto-Zaera , Leonardo Zepeda-Núñez , Michael Lindsey , Norm Tubman , K. Birgitta Whaley , Lin Lin

We propose to calculate spectral functions of quantum impurity models using the Time Evolving Block Decimation (TEBD) for Matrix Product States. The resolution of the spectral function is improved by a so-called linear prediction approach.…

Strongly Correlated Electrons · Physics 2015-10-28 Martin Ganahl , Markus Aichhorn , Patrik Thunström , Karsten Held , Hans Gerd Evertz , Frank Verstraete

Ab initio determination of model Hamiltonian parameters for strongly correlated materials is a key issue in applying many-particle theoretical tools to real narrow-band materials. We propose a self-contained calculation scheme to construct,…

Strongly Correlated Electrons · Physics 2008-09-09 Dm. Korotin , A. V. Kozhevnikov , S. L. Skornyakov , I. Leonov , N. Binggeli , V. I. Anisimov , G. Trimarchi

Nonlocal correlations play an essential role in correlated electron systems, especially in the vicinity of phase transitions and crossovers, where two-particle correlation functions display a distinct momentum dependence. In nonequilibrium…

Strongly Correlated Electrons · Physics 2023-06-29 Olivier Simard , Philipp Werner

For reliable and efficient inclusion of electron-electron correlation effects in nanosystems we propose a combined density-functional-theory/nonhomogeneous dynamical-mean-field-theory (DFT + DMFT) approach which employs an approximate…

Strongly Correlated Electrons · Physics 2013-11-14 Alamgir Kabir , Volodymyr Turkowski , Talat S. Rahman

We describe a recent implementation of the combined GW and dynamical mean field (DMFT) method "GW+DMFT" for the two-dimensional Hubbard model with on-site and nearest-neighbor repulsion. We clarify the relation of the GW+DMFT scheme to…

Strongly Correlated Electrons · Physics 2013-04-01 Thomas Ayral , Silke Biermann , Philipp Werner

A hierarchical equations of motion (HEOM) based numerical approach is developed for accurate and efficient evaluation of dynamical observables of strongly correlated quantum impurity systems. This approach is capable of describing…

Strongly Correlated Electrons · Physics 2013-01-28 ZhenHua Li , NingHua Tong , Xiao Zheng , Dong Hou , JianHua Wei , Jie Hu , YiJing Yan

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study…

Quantum Gases · Physics 2015-05-13 Wen-Jun Hu , Ning-Hua Tong

We here present how a self-consistent solution of the dynamical mean field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or…

Strongly Correlated Electrons · Physics 2014-08-06 Y. Lu , M. Höppner , O. Gunnarsson , M. W. Haverkort
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