An Auxiliary Field Quantum Monte Carlo study of the Hubbard Kanamori model

In the eld of strongly-correlated many-electron systems, the Hubbard Kanamori model has been extensively studied as a prototype for transition-metal oxides, to accurately describe interesting problems like magnetic properties, phase transitions, and unconventional superconductivity. The model is multiorbital in nature and contains Hunds coupling terms. However, due to the sign problem, it is mainly studied in the framework of Dynamical Mean-Field Theory (DMFT). We study the model using the ground state Auxiliary Field Quantum Monte Carlo (AFQMC) method. Different decomposition strategies for the Hunds coupling and pair-exchange terms are proposed for Hubbard-Stratonovich transformation. The Constrained Path Approximation and Phaseless Approximation are used to control the sign and phase problem. Systematic tests are carried out and shown the high accuracy of this approach. The ground state properties of real material Ca₂RuO₄ will be discussed.