Negative sign free formulations of generalized Kitaev models with higher symmetries

TL;DR

This paper introduces a sign-free quantum Monte Carlo method for generalized Kitaev models with higher symmetries, revealing complex phase diagrams and the absence of spin liquid phases in certain symmetry-enhanced models.

Contribution

It develops a negative-sign-free formulation of the auxiliary field quantum Monte Carlo algorithm for generalized Kitaev models with higher symmetries, expanding the applicability of the method.

Findings

Symmetry enhancement allows escape from frustration.

Spin liquid phases are absent in the Z2×SU(2) model.

Rich phase diagram with higher symmetries and quantum critical points.

Abstract

We provide a negative-sign-free formulation of the auxiliary field quantum Monte Carlo algorithm for generalized Kitaev models with higher symmetries. Our formulation is based on the Abrikosov fermion representation of the spin-1/2 degree of freedom and the phase pinning approach [Phys. Rev. B 104, L081106 (2021)]. Enhancing the number of fermion flavors or orbitals from one to $N$ allows one to generalize the inherent $Z_2$ global symmetry to Z$_2$$\times$SU($N$)$_o$. Using this general approach, we study the Z$_2$$\times$SU(2)$_o$ Kitaev-Heisenberg model reflecting the competition between the isotropic Heisenberg exchange and Kitaev-type bond-directional exchange interactions. We show that the symmetry enhancement provides a path to escape frustration and that the spin liquid phases in the original Z$_2$ symmetric model are not present in this model. Nevertheless, the ground-state phase diagram is extremely rich and has points with higher global and local continuous symmetries as well as de-confined quantum critical points.