S. D. Semenov | Searcharxiv

arXiv2026

A Unified Approach to Strong Local Correlations and Collective Fluctuations: Eliminating Divergence in the Spin Channel

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.

cond-mat.str-el↗

arXiv2024

Fluctuating field series: towards calculations of correlated systems with high accuracy

We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for medium-sized lattices. It can be also used as a solver for the cluster approximations for infinite-size lattices. We introduce classical fluctuating field coupled to fermionic collective mode(s). This way, fluctuations in selected modes are treated in a non-perturbative way. Other degrees of freedom are accounted for the diagram expansion performed at each value of the fluctuating field. The method is benchmarked for the $U/t=1$ and $U/t=2$ Hubbard lattices at half-filling. Results for susceptibility in the antiferromagnetic channel along with the single particle density of states are compared with the numerically exact quantum Monte Carlo data. Calculations up to the third order of the series expansion are performed and show a uniform convergence to the reference result for the susceptibility. This convergence is observed well below the DMFT Neél temperature and makes our practically simple method applicable in a much wider temperature range than DMFT-based diagrammatic schemes.

cond-mat.str-el↗