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Kramers-Wannier dualities via symmetries
1Institut de Physique Théorique, Université catholique de Louvain, Chemin du Cyclotron, 2 B-1348, Louvain-La-Neuve, Belgium.
Physical Review Letters
|December 31, 2005
Summary
Kramers-Wannier dualities in lattice models are directly identified through symmetry transformations of boundary states in conformal field theory. Only models with auto-orbifold properties exhibit self-duality transformations.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
Background:
- Kramers-Wannier dualities are fundamental concepts in statistical mechanics and quantum field theory.
- These dualities relate seemingly different lattice models through symmetry transformations.
- Understanding the origin and scope of these dualities is crucial for theoretical physics.
Purpose of the Study:
- To establish a direct and explicit method for identifying Kramers-Wannier dualities.
- To explore the connection between dualities and symmetries in lattice models.
- To investigate the specific properties of models exhibiting self-duality.
Main Methods:
- Analysis of symmetry transformations of boundary states in conformal field theory (CFT).
- Direct derivation of dualities from CFT symmetry properties.
- Classification of lattice models based on their symmetry characteristics.
Main Results:
- A direct method to find Kramers-Wannier dualities from CFT boundary state symmetries is presented.
- The study reveals an intimate connection between dualities and symmetry transformations.
- Models possessing an auto-orbifold property are uniquely identified as those with self-duality transformations.
Conclusions:
- Symmetry transformations of boundary states in CFT provide a direct route to Kramers-Wannier dualities.
- The auto-orbifold property is a key characteristic distinguishing self-dual models.
- This work offers a new perspective on understanding dualities in lattice systems.