Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems

Background:

• The Kosterlitz-Thouless phase transition is crucial for understanding 2D systems.
• Simulating 2D phase transitions with continuous symmetries is computationally challenging.

Purpose of the Study:

• To apply variational tensor-network methods for simulating the 2D XY model's Kosterlitz-Thouless transition.
• To characterize critical phenomena and phases with high precision.

Main Methods:

• Utilized uniform matrix product states (MPS) with non-Abelian O(2) symmetry.
• Analyzed the MPS entanglement spectrum to identify phases.
• Computed spin stiffness and correlation length.

Main Results:

• Accurately computed the universal drop in spin stiffness at the critical point.
• Characterized the Luttinger-liquid phase in the low-temperature regime.
• Confirmed exponential correlation length divergence and precisely estimated the critical temperature.

Conclusions:

• The MPS approach is effective for simulating 2D phase transitions with continuous symmetries.
• This method provides a powerful tool for studying critical phenomena in condensed matter systems.