Kinetic Magnetism and Metallicity in the Triangular Hubbard Model

A new study mapped the phase diagram of the infinite-U triangular Hubbard model (ITHM), investigating the interplay between geometric frustration and finite hole density. Using the density matrix renormalization group (DMRG) algorithm, researchers focused on the stability of the 120° antiferromagnetic (AFM) state — a form of magnetism induced purely by the kinetic energy of charge carriers — and its transitions to other phases under doping.

Kinetic Frustration in Geometric Lattices

The emergence of magnetic ordering in the complete absence of magnetic interactions (such as the $J=0$ limit) is a complex phenomenon. The Nagaoka theorem previously determined that, in bipartite lattices with a single hole and extreme interactions, the system favors a ferromagnetic (FM) background to minimize its energy. However, in frustrated geometries like the triangular lattice, destructive interference in the hole’s hopping pathways suppresses this tendency. Building on the prior work of Haerter and Shastry, which demonstrated that a single hole stabilizes a 120° antiferromagnetic state, the new research sought to determine how this system behaves with multiple holes in a macroscopic regime.

DMRG Analysis and the Intermediate Multimer Phase

To understand the exact nature of this state in the thermodynamic limit, the team performed large-scale DMRG calculations to evaluate the spin structure factor and momentum space occupations. The study revealed that the 120° order survives small dopings, but as the hole density increases beyond the Haerter-Shastry regime, the system enters an intermediate phase. This phase breaks the six-fold rotational symmetry and is characterized by multimers — multiple correlated spins arranged in stripe-like patterns — which, at high doping rates, eventually melt into a paramagnetic state.

“We also find evidence of gapless charge excitations (metallicity) throughout the phase diagram for finite hole density.”

Impact on Solid-State Emulators and Cold Atoms

The results are not limited to the theoretical infinite-$U$ limit, but provide concrete predictions for systems with finite and large values of $U/t$, determining the exact regimes where kinetic frustration crosses over with the classical superexchange mechanism. The identification of continuous metallic properties and the multimer phase has direct applicability in the development and analysis of results obtained in modern Hubbard model emulators, such as ultracold atom optical lattices and solid-state moiré materials like transition metal dichalcogenide layers.