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Quantum 2-body Hamiltonian for topological color codes

✍ Scribed by H. Bombin; M. Kargarian; M.A. Martin-Delgado

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
402 KB
Volume
57
Category
Article
ISSN
0015-8208

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✦ Synopsis

Abstract

We introduce a two‐body quantum Hamiltonian model with spins‐${1 \over 2}$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non‐perturbative effect. The model has a Z~2~Γ— Z~2~ gauge group symmetry and string‐net integrals of motion. There exists a gapped phase in which the low‐energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.

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