Effective Spin Couplings in the Mott Insulator of the Honeycomb Lattice Hubbard Model

TL;DR

This paper derives and tests effective spin Hamiltonians for the Mott insulator phase of the Hubbard model on a honeycomb lattice, revealing dominant six-spin interactions and evaluating their accuracy against numerical results.

Contribution

It introduces a systematic derivation of effective spin models including six-spin interactions and compares their predictions with numerical simulations.

Findings

Six-spin interactions dominate the effective low-energy physics.

A minimal spin model captures most energetic properties.

More complex models show discrepancies at intermediate couplings.

Abstract

Motivated by the recent discovery of a spin liquid phase for the Hubbard model on the honeycomb lattice at half-filling, we apply both perturbative and non-perturbative techniques to derive effective spin Hamiltonians describing the low-energy physics of the Mott-insulating phase of the system. Exact diagonalizations of the so-derived models on small clusters are performed, in order to assess the quality of the effective low-energy theory in the spin-liquid regime. We show that six-spin interactions on the elementary loop of the honeycomb lattice are the dominant sub-leading effective couplings. A minimal spin model is shown to reproduce most of the energetic properties of the Hubbard model on the honeycomb lattice in its spin-liquid phase. Surprisingly, a more elaborate effective low-energy spin model obtained by a systematic graph expansion rather disagrees beyond a certain point with the numerical results for the Hubbard model at intermediate couplings.