Orbital-selective Mott phases of a one-dimensional three-orbital Hubbard model studied using computational techniques

TL;DR

This paper demonstrates that the Constrained-Path Quantum Monte Carlo method can accurately map the phase diagram of a one-dimensional three-orbital Hubbard model, including orbital-selective Mott phases, facilitating future studies in more complex geometries.

Contribution

The study shows that CPQMC, combined with Hartree-Fock trial states, effectively reproduces the phase diagram of a multiorbital Hubbard model, even when simplified by neglecting certain interaction terms.

Findings

CPQMC accurately reproduces the phase diagram of the model.

Neglecting pair-hopping and Hund coupling terms has mild effects on the phase diagram.

Additional DMRG and DQMC confirm the robustness of the results.

Abstract

A recently introduced one-dimensional three-orbital Hubbard model displays orbital-selective Mott phases with exotic spin arrangements such as spin block states [J. Rinc\'on {\em et al.}, Phys. Rev. Lett. \textbf{112}, 106405 (2014)]. In this publication we show that the Constrained-Path Quantum Monte Carlo (CPQMC) technique can accurately reproduce the phase diagram of this multiorbital one-dimensional model, paving the way to future CPQMC studies in systems with more challenging geometries, such as ladders and planes. The success of this approach relies on using the Hartree-Fock technique to prepare the trial states needed in CPQMC. We also study a simplified version of the model where the pair-hopping term is neglected and the Hund coupling is restricted to its Ising component. The corresponding phase diagrams are shown to be only mildly affected by the absence of these technically difficult-to-implement terms. This is confirmed by additional Density Matrix Renormalization Group and Determinant Quantum Monte Carlo calculations carried out for the same simplified model, with the latter displaying only mild Fermion sign problems. We conclude that these methods are able to capture quantitatively the rich physics of the several orbital-selective Mott phases (OSMP) displayed by this model, thus enabling computational studies of the OSMP regime in higher dimensions, beyond static or dynamic mean field approximations.