Corner transfer matrix renormalization group analysis of the two-dimensional dodecahedron model

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Quantum magnetism

Background:

• The classical Heisenberg model exhibits continuous O(3) symmetry.
• Investigating discrete analogs of quantum models is crucial for understanding complex systems.
• Large on-site degrees of freedom pose significant computational challenges.

Purpose of the Study:

• To analyze the phase transition of the dodecahedron model on a square lattice.
• To develop efficient numerical methods for models with large on-site degrees of freedom.
• To determine critical exponents and the central charge of the system.

Main Methods:

• Development of a massively parallelized numerical algorithm.
• Application of the corner transfer matrix renormalization group (CTMRG) method.
• Integration of EigenExa, a high-performance parallelized eigensolver.

Main Results:

• A second-order phase transition was identified at T_{c}=0.4398(8).
• Critical exponents ν=2.88(8) and β=0.21(1) were determined.
• The central charge was estimated to be c=1.99(6).

Conclusions:

• The dodecahedron model exhibits a second-order phase transition.
• The developed parallelized CTMRG method is effective for large on-site degrees of freedom.
• The findings provide insights into quantum magnetism and critical phenomena.