Correlation driven dimensional reduction in a two orbital Hubbard model

We apply a recently developed many-body technique that allows for the incorporation of thermal effects, to a two orbital Hubbard model of relevance for the pnictides. In this ‘Mean Field-Monte Carlo’ (MF-MC) approach, we first perform a mean field (MF) decomposition of the Hubbard model and then treat the mean field parameters via the standard finite-temperature classical Monte Carlo (MC). We have earlier established [1] that for the one orbital Hubbard model, this MF-MC approach provides remarkable improvement over simple finite-temperature mean field methods and is in good agreement with Determinantal Quantum Monte Carlo results. In this talk we will discuss our MC-MF results applied to the two orbital Hubbard model with degenerate dxz and dyz orbitals for the undoped pnictides [2]. The onsite repulsion strength $U$ vs. temperature phase diagram is rich and has a narrow window of nematicity above the N’eel temperature. Our main result is the discovery of a novel intermediate coupling regime characterized by an unexpected spontaneous dimensional reduction that renders one direction insulating and the other metallic. [1] A. Mukherjee, et. al. Phys. Rev. \textbf{B} 90, 205133 (2014). [2] A. Mukherjee, et. al. arXiv: 1510.04902