Topological transition in a two-dimensional three-vector model: A non-Boltzmann Monte Carlo study

Area of Science:

• Condensed Matter Physics
• Materials Science
• Statistical Mechanics

Background:

• Previous studies on (d=2,n=3) lattice models of liquid crystals (LCs) suggested a topological transition to a low-temperature critical state.
• These earlier findings were based on non-Boltzmann Monte Carlo simulations, which indicated a crossover to a nematic phase instead of a topological transition.

Purpose of the Study:

• To investigate the role of symmetry in topological transitions within (d=2,n=3) lattice models of liquid crystals.
• To explore a more restrictive symmetry (Π_{1}(R)=Q, the quaternion group) to understand its impact on defect formation and topological order.

Main Methods:

• Utilized a two-dimensional three-vector (d=2,n=3) lattice model for liquid crystal (LC) systems.
• Assigned a more restrictive symmetry (Π_{1}(R)=Q) to the system's Hamiltonian.
• Employed non-Boltzmann Monte Carlo simulations to analyze the system's behavior at different temperatures.

Main Results:

• A defect-mediated topological transition to a low-temperature phase with topological order was observed under the restrictive quaternion symmetry.
• This phase exhibits quasi-long-range order of its three spin degrees, with a vanishing power-law exponent at zero temperature.
• The high-temperature phase displays exponential spin correlations, with lengths diverging near the topological transition point.

Conclusions:

• The choice of symmetry in the Hamiltonian is crucial for inducing defect-mediated topological transitions in (d=2,n=3) lattice models.
• Biaxial liquid crystal (LC) models, possessing the required symmetry, are proposed as suitable systems to experimentally exhibit these topological transitions.
• The findings challenge previous reports and offer a new mechanism for understanding phase transitions in complex condensed matter systems.