Critical properties of the two-dimensional q-state clock model

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Statistical Mechanics

Background:

• The q-state clock model is a fundamental model in statistical mechanics, exhibiting complex phase transitions.
• Understanding critical phenomena in two-dimensional systems is crucial for theoretical physics.

Purpose of the Study:

• To accurately determine the critical properties of the q-state clock model on a square lattice.
• To identify the universality class of the observed phase transitions.
• To investigate the low-energy physics and conformal properties of the model.

Main Methods:

• State-of-the-art tensor network simulations performed directly in the thermodynamic limit.
• Analysis of the singularity of the classical analog of entanglement entropy to locate phase transitions.
• Numerical evidence to classify the nature of the phase transitions.

Main Results:

• Accurate determination of two distinct phase transition temperatures.
• Classification of both transitions as Berezinskii-Kosterlitz-Thouless (BKT) type for q≥5.
• Confirmation that the low-energy physics is described by Z_{q}-deformed sine-Gordon theory.
• Determination of characteristic conformal parameters, including the compactification radius.

Conclusions:

• The q-state clock model exhibits BKT phase transitions for q≥5.
• The low-energy physics is governed by Z_{q}-deformed sine-Gordon theory.
• Conformal parameters play a key role in describing the critical properties of the intermediate BKT phase.