Variational Mean-field approach to three-body bound states in many- body systems

Motivated by recent dynamical mean-field theory studies on the Hubbard model [Sakai et al., Phys. Rev. B 94, 115130 (2016)], we study the formation of symmetry-breaking three-body bound states in interacting systems. We introduce a new many-body approach, involving resonant Weiss fields that inject a test bound-state into the three body channel. Using a three-body adaptation of Feynman's variational mean-field approach, we are able to put a rigorous bound on the ground state energy of a state with three-body resonances that can be used as the basis for a new kind three-body Hartree Fock approach. This talk will present these new results and will discuss our ongoing efforts to apply it to physical systems, including Abrikosov-Suhl resonance formation in the Anderson impurity model and d-wave superconductivity in the Hubbard model.