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

Sandro Wenzel, Sergey E. Korshunov, K. Penc, Frédéric Mila

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We investigate the ground-state properties of the highly degenerate noncoplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice with Monte Carlo simulations. For that purpose, we introduce an Ising pseudospin representation of the ground states, and we use a simple Metropolis algorithm with local updates, as well as a powerful cluster algorithm. At sizes that can be sampled with local updates, the presence of long-range order is surprisingly combined with an algebraic decay of correlations and the complete disordering of the chirality. It is only thanks to the investigation of unusually large systems (containing ∼108 spins) with cluster updates that the true asymptotic regime can be reached and that the system can be proven to consist of equivalent (i.e., equally ordered) sublattices. These large-scale simulations also demonstrate that the scalar chirality exhibits long-range order at zero temperature, implying that the system has to undergo a finite-temperature phase transition. Finally, we show that the average distance in the order parameter space, which has the structure of an infinite Cayley tree, remains remarkably small between any pair of points, even in the limit when the real space distance between them tends to infinity.

Original languageEnglish
Article number094404
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume88
Issue number9
DOIs
Publication statusPublished - Sep 4 2013

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Chirality
chirality
Crystal lattices
Ground state
ground state
infinity
sublattices
simulation
Phase transitions
scalars
Temperature
temperature
decay
Monte Carlo simulation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Electronic, Optical and Magnetic Materials

Cite this

Zero-temperature Monte Carlo study of the noncoplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice. / Wenzel, Sandro; Korshunov, Sergey E.; Penc, K.; Mila, Frédéric.

In: Physical Review B - Condensed Matter and Materials Physics, Vol. 88, No. 9, 094404, 04.09.2013.

Research output: Contribution to journalArticle

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