FLEX+DMFT approach to thed-wave superconducting phase diagram of the two-dimensional Hubbard model

Abstract

The dynamical mean-field theory (DMFT) combined with the fluctuation exchange (FLEX) method, namely FLEX+DMFT, is an approach for correlated electron systems to incorporate both local and nonlocal long-range correlations in a self-consistent manner. We formulate FLEX+DMFT in a systematic way starting from a Luttinger-Ward functional, and apply it to study the d-wave superconductivity in the two-dimensional repulsive Hubbard model. The critical temperature (Tc) curve obtained in the FLEX+DMFT exhibits a dome structure as a function of the filling, which has not been clearly observed in the FLEX approach alone. We trace back the origin of the dome to the local vertex correction from DMFT that renders a filling dependence in the FLEX self-energy. We compare the results with those of GW+DMFT, where the Tc-dome structure is qualitatively reproduced due to the same vertex correction effect, but a crucial difference from FLEX+DMFT is that Tc is always estimated below the Néel temperature in GW+DMFT. The single-particle spectral function obtained with FLEX+DMFT exhibits a double-peak structure as a precursor of the Hubbard bands at temperatures above Tc.

Parquet decomposition calculations of the electronic self-energy

“…In the last years, also calculations of two-particle vertex functions [20][21][22][23][24][25][26] became possible. This technical progress has a very high impact, because two-particle vertex functions are a crucial ingredient for calculating 13,14 momentum-and frequency-dependent response functions in DMFT and DCA, and also represent the building blocks for all multiscale extensions of DMFT [27][28][29][30][31][32] and DCA, 33,34 aiming at including spatial correlations on all length scales.…”

Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

“…This is far from being a merely academic issue, because many [14][15][16][17][18][19][20][21][22][23] of the cutting edge approaches recently developed to treat strongly correlated electrons in finite (three or two dimensional) systems largely exploit the Feynman diagrammatics and/or the Luttinger-Ward functional formalism. First specific reports about unexpected theoretical consequences induced by the breakdown of the many-body perturbation expansion have been recently presented by several groups.…”

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

“…Thus, on the one hand, we extend the single-site real-space DMFT calculations [62,63,65,66] to include d-wave superconductivity and, on the other, we extend the uniform plaquette DMFT approximation [52][53][54][55]57,58] to include the striped order. We find a wide region of coexistence between striped order and spatially modulated d-wave superconductivity, and analyze the behavior of the superconducting order parameter in the striped states.…”

“…It has been used to gain insight to the Mott transition both in the Hubbard model [49] and in real materials [50]. Since the initial realization [52] that the plaquette DMFT (meaning cellular DMFT [51] with a 2 × 2 cluster) can describe d-wave superconductivity, this approximation has been employed to study the competition and coexistence of superconductivity and magnetic order in the ground state [53,54], the effect of nearest-neighbor repulsion [55,56], and finite temperature energetics and critical temperatures of the superconductivity [57,58]. This approximation in its basic form cannot produce a striped state, since the 2 × 2 unit cell does not allow modulation of the magnetization across the lattice.…”