The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux

Abstract: We consider a half-filled system of spin-1/2 fermions on a triangular ladder with spin-dependent hopping in the presence of spin-dependent flux. Using the Schrieffer-Wolff transformation, we derive an effective spin Hamiltonian describing the infrared properties of the system in the limit of strong on-site repulsion. The expansion is performed up to the third order in the hopping amplitude over on-site interaction energy. It is shown that the low-energy spin excitations are described by an anisotropic $XXZ$ Heisenberg model with Dzyaloshinskii-Moriya interaction and an unconventional three-spin (correlated exchange) term in the presence of an extended magnetic field. The latter couples not only to $z$-projection of the total spin on a triangular plaquette but also to the product of $z$-components of three spins located on vertices of the triangle. In the case of strong attractive interaction, the corresponding effective model is derived from the repulsive one using the one-spin-component particle-hole transformation. The effective Hamiltonian is given by the same $XXZ$ Heisenberg model, as in the repulsive case, but in terms of pseudospin (charge) operators.