Quantum 2-Body Hamiltonian for Topological Color Codes

Abstract

We introduce a two-body quantum Hamiltonian model with spins-$\half$ 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 ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ 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.

Cotribution to the Proceedings of the Scala Conference 2009 (Cortina, Italy). Special Issue dedicated to Prof. Prof. Tombesi, on occasion of his seventieth birthday. Editors: D. Vitali, I Marzoli, S. Mancini, G. Di Giuseppe. "Fortschritte der Physik"

References in corpus (6)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Topological Quantum Distillation
• Topological Computation without Braiding
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Anyonic interferometry and protected memories in atomic spin lattices
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Cited by in corpus (5)

• Feasibility of self-correcting quantum memory and thermal stability of topological order
• Quantum computation from dynamic automorphism codes
• Quantum codes give counterexamples to the unique pre-image conjecture of the N-representability problem
• Generalized Color Codes Supporting Non-Abelian Anyons
• Implementation of Single-qubit and CNOT Gates by Anyonic Excitations of Two-body Topological Color Code