Topological order in an exactly solvable 3D spin model

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.11.002· OSTI ID:21579876

Bravyi, Sergey ^[1]; Leemhuis, Bernhard ^[2]; Terhal, Barbara M ^[1]

---

1. IBM Watson Research Center, Yorktown Heights, NY 10598 (United States)
2. Institute for Theoretical Physics, University of Amsterdam, Postbus 94485, 1090 GL Amsterdam (Netherlands)

Research highlights: RHtriangle We study exactly solvable spin model with six-qubit nearest neighbor interactions on a 3D face centered cubic lattice. RHtriangle The ground space of the model exhibits topological quantum order. RHtriangle Elementary excitations can be geometrically described as the corners of rectangular-shaped membranes. RHtriangle The ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. RHtriangle Logical operators acting on the encoded qubits are described in terms of closed strings and closed membranes. - Abstract: We study a 3D generalization of the toric code model introduced recently by Chamon. This is an exactly solvable spin model with six-qubit nearest-neighbor interactions on an FCC lattice whose ground space exhibits topological quantum order. The elementary excitations of this model which we call monopoles can be geometrically described as the corners of rectangular-shaped membranes. We prove that the creation of an isolated monopole separated from other monopoles by a distance R requires an operator acting on {Omega}(R{sup 2}) qubits. Composite particles that consist of two monopoles (dipoles) and four monopoles (quadrupoles) can be described as end-points of strings. The peculiar feature of the model is that dipole-type strings are rigid, that is, such strings must be aligned with face-diagonals of the lattice. For periodic boundary conditions the ground space can encode 4g qubits where g is the greatest common divisor of the lattice dimensions. We describe a complete set of logical operators acting on the encoded qubits in terms of closed strings and closed membranes.

• OSTI ID: 21579876
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 4; Other Information: DOI: 10.1016/j.aop.2010.11.002; PII: S0003-4916(10)00191-0; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
DIPOLES
EXACT SOLUTIONS
EXCITATION
FCC LATTICES
INTERACTIONS
MONOPOLES
OMEGA BARYONS
PERIODICITY
QUADRUPOLES
QUBITS
SPIN
TOPOLOGY
ANGULAR MOMENTUM
BARYONS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
CUBIC LATTICES
ELEMENTARY PARTICLES
ENERGY-LEVEL TRANSITIONS
FERMIONS
HADRONS
HYPERONS
INFORMATION
MATHEMATICAL SOLUTIONS
MATHEMATICS
MULTIPOLES
PARTICLE PROPERTIES
QUANTUM INFORMATION
STRANGE PARTICLES
VARIATIONS