scholarly journals Cluster-based mean-field and perturbative description of strongly correlated fermion systems: Application to the one- and two-dimensional Hubbard model

2015 ◽  
Vol 92 (8) ◽  
Author(s):  
Carlos A. Jiménez-Hoyos ◽  
Gustavo E. Scuseria
Keyword(s):  
Hubbard Model ◽  
Mean Field ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
Fermion Systems ◽  
The One

SPIN-CARRYING SLAVE BOSON REPRESENTATION FOR STRONGLY CORRELATED FERMION SYSTEMS

1989 ◽  
Vol 03 (12) ◽  
pp. 1833-1842
Author(s):  
P. Wölfle
Keyword(s):  
Hubbard Model ◽  
Anderson Model ◽  
Degrees Of Freedom ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Strongly Correlated ◽  
Dynamical Correlation ◽  
Fermion Systems ◽  
Boson Representation

We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.

scholarly journals High harmonic generation in two-dimensional Mott insulators

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Christopher Orthodoxou ◽  
Amelle Zaïr ◽  
George H. Booth
Keyword(s):  
Quantum Monte Carlo ◽  
Strong Field ◽  
High Harmonic ◽  
Mean Field ◽  
Laser Pulses ◽  
Two Dimensions ◽  
Mott Insulators ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
Mean Field Model

AbstractWith a combination of numerical methods, including quantum Monte Carlo, exact diagonalization, and a simplified dynamical mean-field model, we consider the attosecond charge dynamics of electrons induced by strong-field laser pulses in two-dimensional Mott insulators. The necessity to go beyond single-particle approaches in these strongly correlated systems has made the simulation of two-dimensional extended materials challenging, and we contrast their resulting high-harmonic emission with more widely studied one-dimensional analogues. As well as considering the photo-induced breakdown of the Mott insulating state and magnetic order, we also resolve the time and ultra-high-frequency domains of emission, which are used to characterize both the photo-transition, and the sub-cycle structure of the electron dynamics. This extends simulation capabilities and understanding of the photo-melting of these Mott insulators in two dimensions, at the frontier of attosecond non-equilibrium science of correlated materials.

Quantum phase transitions in two-dimensional strongly correlated fermion systems

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
An Bao ◽  
Yao-Hua Chen ◽  
Heng-Fu Lin ◽  
Hai-Di Liu ◽  
Xiao-Zhong Zhang
Keyword(s):  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Strongly Correlated ◽  
Two Dimensional ◽  
Fermion Systems

scholarly journals ANDERSON LOCALIZATION VS. MOTT–HUBBARD METAL–INSULATOR TRANSITION IN DISORDERED, INTERACTING LATTICE FERMION SYSTEMS

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1727-1755 ◽  
Author(s):  
Krzysztof Byczuk ◽  
Walter Hofstetter ◽  
Dieter Vollhardt
Keyword(s):  
Anderson Localization ◽  
Mean Field Theory ◽  
Mean Field ◽  
Antiferromagnetic Order ◽  
Strongly Correlated ◽  
Theoretical Understanding ◽  
Particle Correlation ◽  
Fermion Systems ◽  
Disordered Lattice ◽  
Lattice Fermion

We review recent progress in our theoretical understanding of strongly correlated fermion systems in the presence of disorder. Results were obtained by the application of a powerful nonperturbative approach, the dynamical mean-field theory (DMFT), to interacting disordered lattice fermions. In particular, we demonstrate that DMFT combined with geometric averaging over disorder can capture Anderson localization and Mott insulating phases on the level of one-particle correlation functions. Results are presented for the ground state phase diagram of the Anderson–Hubbard model at half-filling, both in the paramagnetic phase and in the presence of antiferromagnetic order. We find a new antiferromagnetic metal which is stabilized by disorder. Possible realizations of these quantum phases with ultracold fermions in optical lattices are discussed.

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