Quantum to classical mapping of the two-dimensional toric code in an external field
Sydney R. Timmerman, Zvonimir Z. Bandic, Roger G. Melko
SciPost Phys. Lect. Notes 57 (2022) · published 20 July 2022
- doi: 10.21468/SciPostPhysLectNotes.57
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Abstract
Kitaev's toric code Hamiltonian in dimension D=2 has been extensively studied for its topological properties, including its quantum error correction capabilities. While the Hamiltonian is quantum, it lies within the class of models that admits a D+1 dimensional classical representation. In these notes, we provide details of a Suzuki-Trotter expansion of the partition function of the toric code Hamiltonian in the presence of an external magnetic field. By coupling additional degrees of freedom in the form of a matter field that can subsequently be gauged away, we explicitly derive a classical Hamiltonian on a cubic lattice which takes the form of a non-isotropic 3D Ising gauge theory.
Cited by 2
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Sydney R. Timmerman,
- 2 Zvonimir Bandic,
- 1 3 Roger G. Melko
- 1 Institut Périmètre de physique théorique / Perimeter Institute [PI]
- 2 Western Digital
- 3 University of Waterloo [UW]