Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions

Abstract

We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to $L=512$. Based on the new algorithm we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.

10 pages, 8 figures; version as published

References in corpus (16)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• First order phase transition in the anisotropic quantum orbital compass model
• Evidence of Unconventional Universality Class in a Two-Dimensional Dimerized Quantum Heisenberg Model
• Make life simple: unleash the full power of the parallel tempering algorithm
• Monte Carlo simulations of the directional-ordering transition in the two-dimensional classical and quantum compass model
• Nature of the Quantum Phase Transition in Quantum Compass Model
• Critical Binder cumulant of two-dimensional Ising models
• Multicriticality and entanglement in the one-dimensional quantum compass model
• Topologically decoherence-protected qubits with trapped ions
• Dilution Effects in Two-dimensional Quantum Orbital System
• Quantum phase transition in the one-dimensional period-two and uniform compass model
• Anisotropy of the interface tension of the three-dimensional Ising model
• Finite-Temperature Néel Ordering of Fluctuations in a Plaquette Orbital Model
• Thermal Canting of Spin-Bond Order

Cited by in corpus (4)

• Spin-orbital resonating valence bond liquid on a triangular lattice: Evidence from finite-cluster diagonalization
• Orbital ordering in e_g orbital systems: Ground states and thermodynamics of the 120 degree model
• Entangled spin-orbital phases in the bilayer Kugel-Khomskii model
• Unveiling the nature of three dimensional orbital ordering transitions: the case of $e_g$ and $t_{2g}$ models on the cubic lattice