Effective spin model for the spin-liquid phase of the Hubbard model on the triangular lattice

TL;DR

This paper derives an effective spin model for the spin-liquid phase of the half-filled Hubbard model on a triangular lattice, using high-order perturbative methods, and confirms its accuracy through numerical analysis, revealing a gapless spinon Fermi surface.

Contribution

The paper introduces a high-order strong coupling expansion to derive a pure spin model for the Hubbard model's spin-liquid phase, providing a quantitative and analytical framework.

Findings

Effective spin model accurately describes the spin-liquid phase.

Transition involves a jump in double occupancy.

Evidence suggests a gapless spectrum with a spinon Fermi surface.

Abstract

We show that the spin liquid phase of the half-filled Hubbard model on the triangular lattice can be described by a pure spin model. This is based on a high-order strong coupling expansion (up to order 12) using perturbative continuous unitary transformations. The resulting spin model is consistent with a transition from three-sublattice long-range magnetic order to an insulating spin liquid phase, and with a jump of the double occupancy at the transition. Exact diagonalizations of both models show that the effective spin model is quantitatively accurate well into the spin liquid phase, and a comparison with the Gutzwiller projected Fermi sea suggests a gapless spectrum and a spinon Fermi surface.