Dual boson approach to collective excitations in correlated fermionic systems

Abstract

We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to "bare" RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.

Spin-boson coupling in continuous-time quantum Monte Carlo

“…As in the pure bosonic system, we evaluate the regular part χ reg (0) defined in Eq. (21), which expresses the contribution after subtraction of the Curie term. It turns out from Fig.…”

“…To see this, we evaluate the effective moment M by subtracting χ reg from χ in Eq. (21), and plot it as a function of g in Fig. 6.…”

“…This bosonic dynamical "bath" is determined self-consistently, and thus gives descriptions of a quantum spin glass in infinite dimensions, [10][11][12][13] fluctuations around the molecular field in the (nonrandom) Heisenberg model, [14] and an impurity embedded in an antiferromagnet. [15] With a fermionic bath in terms of DMFT, [16] doping of the spin glass [17] and an extended Hubbard model with intersite interactions [18][19][20][21] can be addressed beyond the molecular-field approximation.…”

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

“…These shortcomings are alleviated in the recently developed dual-boson (DB) method [34], which, in its full-fledged implementation [35,36], computes the susceptibility [11,12] after resumming an infinite number of ladder diagrams built from local impurity four-leg vertices.…”

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.…”