Zero-temperature Monte Carlo study of the non-coplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice

摘要

We investigate the ground-state properties of the highly degeneratenon-coplanar phase of the classical bilinear-biquadratic Heisenberg model onthe triangular lattice with Monte Carlo simulations. For that purpose, weintroduce an Ising pseudospin representation of the ground states, and we use asimple Metropolis algorithm with local updates, as well as a powerful clusteralgorithm. At sizes that can be sampled with local updates, the presence oflong-range order is surprisingly combined with an algebraic decay ofcorrelations and the complete disordering of the chirality. It is only thanksto the investigation of unusually large systems (containing $\sim 10^8$ spins)with cluster updates that the true asymptotic regime can be reached and thatthe system can be proven to consist of equivalent (i.e., equally ordered)sublattices. These large-scale simulations also demonstrate that the scalarchirality exhibits long-range order at zero temperature, implying that thesystem has to undergo a finite-temperature phase transition. Finally, we showthat the average distance in the order parameter space, which has the structureof an infinite Cayley tree, remains remarkably small between any pair ofpoints, even in the limit when the real space distance between them tends toinfinity.