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

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 similar to 10(8) 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.

Ground states and excitations of frustrated magnetic systems, from the classical limit to the quantum case

The first part of this thesis is devoted to classical magnetic systems. A method for an exhaustive search of states that do not break any spatial symmetry on a given lattice is presented. New Néel states on the kagome lattice are described. Their static structure factors give a way to analyze experimental results. Some non-coplanar spin orders are the only ground states of Heisenberg Hamiltonians. The chirality is a discrete order parameter and give rise to a finite temperature phase transition, studied on a toy model. We show that Z2 topological defects proliferate near chirality domain walls. The order of the transition (first order or Ising like) depends on the spin interactions. The Schwinger boson mean-field theory (SBMFT) allows us to link classical and quantum spin physics: long-range ordered and disordered phases as topological spin liquids can be described in this frame. Symmetry and the way to impose them are analyzed. Different phases are distinguished by their fluxes. These are gauge invariant quantities having a signification as well in a quantum system as in the classical limit. Visons are quantum excitations that change fluxes. Thus, the Z2 vorticies are their classical limit. By relaxing some symmetry constraints, chiral phases are obtained, whose classical limit sends back to the first chapter of this thesis, and whose disordered phase gives chiral spin liquids. The example of the Dzyaloshinskii-Moriya interaction on the kagome lattice is studied.

LPTMC, Paris VI2010

Dimensional crossover in the SU(4) Heisenberg model in the six-dimensional antisymmetric self-conjugate representation revealed by quantum Monte Carlo and linear flavor-wave theory

Francisco Hyunkyu Kim, Frédéric Mila, Karlo Penc

Using linear flavor-wave theory (LFWT) and auxiliary field quantum Monte Carlo (QMC), we investigate the properties of the SU(4) Heisenberg model on the anisotropic square lattice in the fully antisymmetric six-dimensional irreducible representation, a model that describes interacting fermions with four flavors at half-filling. Thanks to the calculations on very large systems, we have been able to convincingly demonstrate that QMC results are consistent with a small but finite antiferromagnetic moment at the isotropic point, in qualitative agreement with LFWT obtained earlier [F. H. Kim et al., Phys. Rev. B 96, 205142 (2017)], and in quantitative agreement with results obtained previously on the Hubbard model [D. Wang et al., Phys. Rev. Lett. 112, 156403 (2014)] after extrapolation to infinite U/t. The presence of a long-range antiferromagnetic order has been further confirmed by showing that a phase transition takes place into a valence-bond solid (VBS) phase not too far from the isotropic point when reducing the coupling constant along one direction on the way to decoupled chains.

AMER PHYSICAL SOC2019

Monte Carlo study of the critical properties of the three-dimensional 120 degrees model

Sandro Wenzel

We report on large scale finite-temperature Monte Carlo simulations of the classical 120 degrees or e(g) orbital-only model on the simple cubic lattice in three dimensions with a focus towards its critical properties. This model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent nu approximate to 0.665 is close to the 3D XY value, the exponent eta approximate to 0.15 differs substantially from O(N) values. We also introduce a discrete variant of the e(g) model, called the e(g)-clock model, which is found to display the same set of exponents. Further, an emergent U( 1) symmetry is found at the critical point T-c, which persists for T < T-c below a crossover length scaling as Lambda similar to xi(a), with an unusually small a approximate to 1.3.

2011