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Journal of the Physical Society of Japan

Extension of Dynamical Mean-Field Theory: Inclusion of Spatial Fluctuations

Hiroaki Kusunose

Published Jan 3, 2008• 0 citations
Publisher

Abstract

A hybrid approach that takes account of local and spatial fluctuations is proposed for strongly correlated electron systems. The spatial fluctuations are constructed in the framework of dynamical mean-field theory (DMFT), and they are utilized to improve the DMFT self-energy with nonlocal corrections via the exchange of the fluctuations. We demonstrate that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. Some future applications of the present theory are briefly discussed.

DOI
10.1143/jpsjs.77sa.202

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A hybrid approach that takes account of local and spatial fluctuations is proposed for strongly correlated electron systems. The spatial fluctuations are constructed in the framework of dynamical mean-field theory (DMFT), and they are utilized to improve the DMFT self-energy with nonlocal corrections via the exchange of the fluctuations. We demonstrate that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. Some future applications of the present theory are briefly discussed.
We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of the iterated perturbation theory is proposed and examined. Using the formalism, it is demonstrated that the one-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior in the central coherent quasiparticle peak due to the critical antiferromagnetic fluctuation. The specific heat is considerably enhanced by the short-range order, which assists a tendency of the Mott localization showing the reduction of the double occupancy. We briefly discuss a formulation for the superconducting transition temperature in the present approximation.
An effect of antiferromagnetic fluctuations on single-particle excitations is examined on the basis of an extended dynamical mean-field theory that takes account of long-range spin fluctuations onto the local self energy. We demonstrate that the single-particle spectral intensity in the two-dimensional Hubbard model at half-filling exhibits the pseudo-gap behavior near the Fermi energy due to the critical antiferromagnetic fluctuations. We also show that for the symmetric case in the Anderson lattice model, the hybridized-band gap is enlarged by the antiferromagnetic fluctuations. In both models the antiferromagnetic fluctuations suppress the double occupancy of the correlated electrons.
A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron correlation the one-electron Green's function is strongly spatially damped so that its intersite matrix elements may be considered as small perturbations. Because the non-local corrections are at least quadratic in these matrix elements, DMFT in such cases may be a very accurate approximation in dimensions d = 1-3. This observation provides a rigorous justification for the application of DMFT to physical systems. Furthermore, the technique allows for a systematic evaluation of the nonlocal corrections. This is illustrated with the calculation of the magnetic short range order parameter for nearest neighbor spins in the half filled Hubbard model on the square lattice in its insulating phase which exhibits an excellent agreement with the results of a recent cluster approach.As a second example we study the lowest order correction to the DMFT self-energy and its influence on the local density of states.
Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose a novel extended approach, which we term fluctuating dynamical mean-field theory (fDMFT). It incorporates collective fluctuations of auxiliary impurity models across different sites via functional integration. Technically, this method involves obtaining a family of DMFT solutions on a grid for a self-consistent auxiliary classical field applied to the lattice. While the result can, in principle, be improved diagrammatically, we find that the minimal version of the theory already yields accurate results, with lowest-order diagrammatic corrections offering only minor improvements. This consistent framework, based on our fluctuating local field concept, demonstrates superior performance for the nearly half-filled Hubbard model compared to other known diagrammatic extensions of DMFT.
We investigate the two-dimensional Hubbard model using a real-frequency implementation of the TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT approach. This hybrid method combines the nonlocal correlations captured by the two-particle self-consistent (TPSC) approach with the local dynamical correlations of dynamical mean field theory (DMFT). The results demonstrate that TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT effectively describes pseudogap physics and nonlocal fluctuations in the moderately correlated regime, while also reproducing the Mott insulating state at larger interaction strengths. For doped Mott insulators, we find that TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT captures the evolution of Fermi pockets into Fermi arcs, consistent with the results from cluster DMFT and photoemission studies. These findings highlight the capability of TPSC+DMFT\mathrm{TPSC}+\mathrm{DMFT}TPSC+DMFT to bridge the gap between weak and strong coupling physics in Hubbard models, providing insights into spin and charge fluctuations, as well as their role in the pseudogap formation.
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 settings, the effect of nonlocal correlations on dynamical phase transitions, prethermalization phenomena, and trapping in metastable states is not well understood. In this paper, we introduce a dynamical mean field theory (DMFT) extension to the nonequilibrium two-particle self-consistent (TPSC) approach, which allows to perform nonequilibrium simulations capturing short- and long-ranged nonlocal correlations in the weak-, intermediate-, and strong-correlation regimes. The method self-consistently computes local spin and charge vertices, from which a momentum-dependent self-energy is constructed. Replacing the local part of the self-energy by the DMFT result within this self-consistent scheme provides an improved description of local correlation effects. We explain the details of the formalism and the implementation, and demonstrate the versatility of DMFT+TPSC with interaction quenches and dimensional crossovers in the Hubbard model.