In the study of strongly correlated, many-electron systems, the Hubbard-Kanamori (HK) model has emerged as one of the prototypes for transition metal oxide physics. The model is multiband in nature and contains Hund's coupling terms, which have pronounced effects on metal-insulator transitions, high-temperature superconductivity, and other physical properties. In the following, we present a complete theoretical framework for treating the HK model using the ground-state auxiliary field quantum Monte Carlo (AFQMC) method and analyze its performance on few-band models whose parameters approximate those observed in ruthenates, rhodates, and other materials exhibiting Hund's physics. Unlike previous studies, the constrained path and phaseless approximations are used to respectively control the sign and phase problems, which enables high-accuracy modeling of the HK model's ground-state properties within parameter regimes of experimental interest. We demonstrate that, after careful consideration of the Hubbard-Stratonovich transformations and trial wave functions employed, relative errors in the energy of less than
1 can routinely be achieved for moderate to large values of the Hund's coupling constant. Crucially, our methodology also accurately predicts magnetic ordering and phase transitions. The results presented open the door to more predictive modeling of Hund's physics within a wide range of strongly correlated materials using AFQMC.
We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi auxiliary-field quantum Monte Carlo (BFAFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in the BFAFQMC algorithm. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand the BFAFQMC algorithm's reach. This algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems.