Magnetic phases of the anisotropic triangular Hubbard model from the ghost-Gutzwiller approximation in the rotating spin-frame

TL;DR

This paper introduces the ghost-Gutzwiller approximation as an efficient method to accurately map magnetic phases in the anisotropic triangular Hubbard model, improving upon standard GA and aligning closely with DMFT results.

Contribution

The study develops and benchmarks ghost-GA, demonstrating its ability to incorporate dynamical effects and accurately predict magnetic phases in frustrated systems.

Findings

Ghost-GA significantly improves quantitative agreement with DMFT.

Standard GA overestimates magnetic order stability.

The phase diagram includes paramagnetic and various magnetic phases, excluding 1D antiferromagnetism.

Abstract

We investigate the magnetic phase diagram of the half-filled Hubbard model on the anisotropic triangular lattice using the Gutzwiller approximation (GA) and its ghost generalization (ghost-GA). By combining a rotating spin-frame formulation with high-resolution momentum grids, we determine magnetic ground states through direct total-energy minimization over the ordering wavevector. We benchmark standard GA and ghost-GA against dynamical mean-field theory (DMFT) and dual-fermion results. We show that GA already captures the qualitative structure of the phase diagram, but systematically overestimates the stability of magnetic order due to the absence of dynamical fluctuations. We find that introducing a small number of auxiliary ''ghost'' orbitals is sufficient to recover most dynamical effects and significantly improves quantitative agreement with DMFT. Exploring the full Brillouin zone, we obtain a phase diagram comprising paramagnetic and various magnetic phases. In contrast to ladder dual-fermion susceptibility-based predictions, we find that the one-dimensional antiferromagnetic phase is never stabilized, despite being the leading instability in certain regimes. Our results establish ghost-GA as an efficient and systematically improvable framework for studying magnetism in frustrated systems, capable of achieving near-DMFT accuracy at a fraction of the computational cost. They also highlight that standard GA performs qualitatively well for capturing the general phase diagram, enabling the investigation of incommensurate magnetic orders in more complex systems.