A new approach to strongly correlated fermion systems: the spin–particle–hole coherent-state path integral

Abstract

We describe a new path integral approach to strongly correlated fermion systems, considering the Hubbard model as a specific example. Our approach is based on the introduction of spinparticle-hole coherent states which generalize the spin-1 2 coherent states by allowing the creation of a hole or an additional particle. The action of the fermion system S[γ * , γ; Ω] can be expressed as a function of two Grassmann variables (γ ↑ ,γ ↓ ) describing particles propagating in the lower and upper Hubbard bands, and a unit vector field Ω whose dynamics arises from spin fluctuations. In the strong correlation limit, S[γ * , γ; Ω] can be truncated to quartic order in the fermionic fields and used as the starting point of a strong-coupling diagrammatic expansion in t/U (t being the intersite hopping amplitude and U the on-site Coulomb repulsion). We discuss possible applications of this formalism and its connection to the t-J model and the spin-fermion model.

Dual fermion method as a prototype of generic reference-system approach for correlated fermions

“…This has been pointed out already in the Ref. [32]. The dual self-energy Σ fulfills this requirement by construction.…”

Spin dynamics of itinerant electrons: local magnetic moment formation and Berry phase

“…Description of the spin dynamics, which has not been performed in these works, is a non-trivial task that requires a careful separation of the precession of the vector spin field from the fluctuation of the absolute value of the local magnetic moment. To this effect, we deviate from the main route of these works and make a transformation to a rotating frame for original fermionic variables c * iτ → c * iτ R iτ and c iτ → R † iτ c iτ introducing a unitary rotation matrix in the spin space [33][34][35][36]…”

Contour-time approach to the Bose–Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree–Fock–Bogoliubov level

“…diagrams that contain internal inverse bare propagator lines. Such diagrams have no physical meaning and should not contribute to the physical quantities [95]. It should be noted that in addition to the physical diagrams, the u vertices also generate "anomalous" terms.…”