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In the study of strongly-correlated, many-electron systems, the HubbardKanamori (HK) model has emerged as one of the prototypes for transition metaloxide physics. The model is multi-band in nature and contains Hund's couplingterms, which have pronounced effects on metal-insulator transitions,high-temperature superconductivity, and other physical properties. In thefollowing, we present a complete theoretical framework for treating the HKmodel using the ground state Auxiliary Field Quantum Monte Carlo (AFQMC) methodand analyze its performance on few-band models whose parameters approximatethose observed in ruthenate, rhodates, and other materials exhibiting Hund'sphysics. Unlike previous studies, the constrained path and phaselessapproximations are used to respectively control the sign and phase problems,which enables high accuracy modeling of the HK model's ground state propertieswithin parameter regimes of experimental interest. We demonstrate that, aftercareful consideration of the Hubbard-Stratonovich transformations and trialwave functions employed, relative errors in the energy of less than 1% canroutinely be achieved for moderate to large values of the Hund's couplingconstant. Crucially, our methodology also accurately predicts magnetic orderingand phase transitions. The results presented open the door to more predictivemodeling of Hund's physics within a wide range of strongly-correlated materialsusing AFQMC.

Auxiliary Field Quantum Monte Carlo for Multiband Hubbard Models: Controlling the Sign and Phase Problems to Capture Hund's Physics