TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysLectNotes.57
TI  - Quantum to classical mapping of the two-dimensional toric code in an external field
PY  - 2022/07/20
UR  - https://www.scipost.org/SciPostPhysLectNotes.57
JF  - SciPost Physics Lecture Notes
JA  - SciPost Phys. Lect. Notes
SP  - 57
A1  - Timmerman, Sydney R.
AU  - Bandic, Zvonimir
AU  - Melko, Roger G.
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysLectNotes.57,
	title={{Quantum to classical mapping of the two-dimensional toric code in an external field}},
	author={Sydney R. Timmerman and  Zvonimir Z. Bandic and Roger G. Melko},
	journal={SciPost Phys. Lect. Notes},
	pages={57},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.57},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.57},
}