In:
SciPost Physics Lecture Notes, Stichting SciPost
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.
Type of Medium:
Online Resource
ISSN:
2590-1990
DOI:
10.21468/SciPostPhysLectNotes
DOI:
10.21468/SciPostPhysLectNotes.57
Language:
Unknown
Publisher:
Stichting SciPost
Publication Date:
2022
detail.hit.zdb_id:
2934601-0
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