Berezinskii-Kosterlitz-Thouless Paired Phase in Coupled XY Models

Area of Science:

• Condensed matter physics
• Topological phases of matter
• Statistical mechanics

Background:

• Two-dimensional systems can exhibit the Berezinskii-Kosterlitz-Thouless (BKT) transition.
• In the uncoupled limit, these systems display distinct phases characterized by algebraic or exponential decay of correlation functions.

Purpose of the Study:

• Investigate the impact of linear tunneling coupling on systems exhibiting BKT transitions.
• Identify emergent phases and their correlation properties under coupling.
• Map the phase diagram of coupled topological systems.

Main Methods:

• Theoretical analysis of linear tunneling coupling between two-dimensional systems.
• Numerical simulations of two coupled XY models at finite temperatures.
• Renormalization group approach to characterize the phase diagram.

Main Results:

• A novel BKT-paired phase emerges when linear coupling is introduced.
• This phase is characterized by exponentially decaying one-body correlations and power-law decaying two-body correlations.
• Numerical evidence confirms the presence of the BKT-paired phase for any finite interlayer coupling.

Conclusions:

• Linear coupling between BKT systems can lead to new topological phases.
• The BKT-paired phase represents a distinct state of matter with unique correlation behaviors.
• The findings provide a comprehensive understanding of phase transitions in coupled topological systems.