Tensor renormalization group study of classical XY model on the square lattice

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Quantum Field Theory

Background:

• The continuous XY model is a fundamental model in statistical mechanics.
• Understanding its thermodynamic properties and phase transitions is crucial for various physical systems.

Purpose of the Study:

• To investigate the thermodynamic properties of the continuous XY model on a square lattice.
• To determine the Kosterlitz-Thouless transition temperature and critical exponent delta.

Main Methods:

• Employed the tensor renormalization group (TRG) method.
• Utilized higher-order singular value decomposition (HOSVD) within the TRG framework.
• Compared results with Monte Carlo (MC) simulations and high-temperature series expansion (HTSE).

Main Results:

• Temperature dependence of free energy, internal energy, and specific heat showed agreement with MC calculations.
• The Kosterlitz-Thouless transition temperature was determined to be 0.8921(19).
• The critical exponent delta was estimated at 14.5 at the transition temperature.

Conclusions:

• The TRG method, combined with HOSVD, accurately reproduces thermodynamic properties of the XY model.
• The calculated transition temperature and critical exponent are consistent with existing theoretical and computational results.