Generalized spin density wave state of the Hubbard model on the C12 and C60 clusters

TL;DR

This study investigates the Hubbard model on C12 and C60 clusters, revealing a spin-ordered phase at intermediate coupling and analyzing excitations, with implications for superconductivity in doped fullerenes.

Contribution

It introduces a generalized spin density wave state for the Hubbard model on specific clusters and analyzes the transition from paramagnetic to spin-ordered phases.

Findings

Magnetic-like instability at (U/t)_c ≈ 2.6

Spin arrangement similar to classical Heisenberg model

Indicates a crossover between paramagnetic and spin-correlated regimes

Abstract

The one-band Hubbard model at half-filling on a truncated tetrahedron (C$_{12}$), and on the C$_{60}$ molecule is studied. Within the Hartree-Fock approximation, we find a magnetic-like instability of the `Fermi sea' towards a spin-ordered phase for an intermediate value of the coupling ${\rm (U/t)_c}\approx 2.6$. The ordered phase presents a spin arrangement similar to that of the classical Heisenberg model defined on the same clusters. We study the linear excitations around the Hartree-Fock ground states using the random-phase approximation. On a finite cluster, we expect that these results signal the presence of a $rapid$ $crossover$ between a paramagnetic region and a regime where spin correlations are important. The relationship with the Heisenberg limit (large ${\rm U/t}$) is discussed. Finally, we comment on implications of our results for purely repulsive models of superconductivity in alkali-metal-doped fullerenes.