Loop algorithm for Heisenberg models with biquadratic interaction and phase transitions in two dimensions

Abstract

We present a new algorithm for quantum Monte Carlo simulation based on global updating with loops. While various theoretical predictions are confirmed in one dimension, we find, for S=1 systems on a square lattice with an antiferromagnetic biquadratic interaction, that the intermediate phase between the antiferromagnetic and the ferromagnetic phases is disordered and that the two phase transitions are both of the first order in contrast to the one-dimensional case. It is strongly suggested that the transition points coincide those at which the algorithm changes qualitatively.

4 pages including 4 figures, to appear in JPSJ

Cited by in corpus (16)

• Recent Developments of World-Line Monte Carlo Methods
• Néel and Spin-Peierls ground states of two-dimensional SU(N) quantum antiferromagnets
• Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction
• Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice
• Dimer-Quadrupolar Quantum Phase Transition in the Quasi-One-Dimensional Heisenberg Model with Biquadratic Interaction
• Spin nematic ground state of the triangular lattice S=1 biquadratic model
• Spin dynamics of the bilinear-biquadratic $S=1$ Heisenberg model on the triangular lattice: a quantum Monte Carlo study
• Symmetry-protected topological order and negative-sign problem for SO(N) bilinear-biquadratic chains
• Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems
• Spin-$S$ designer hamiltonians and the square lattice $S=1$ Haldane nematic
• The bilinear-biquadratic model on the complete graph
• Finite temperature thermodynamic properties of the spin-1 nematics in an applied magnetic field
• Magnetism in spin crossover systems: short-range order and effects beyond the Heisenberg model
• Topological edge states in spin 1 bilinear-biquadratic model
• Identification of gapless phases by a twisting operator
• Diffusion in the Continuous-Imaginary-Time Quantum World-Line Monte Carlo Simulations with Extended Ensembles