String-net condensation: A physical mechanism for topological phases
- Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)
We show that quantum systems of extended objects naturally give rise to a large class of exotic phases--namely topological phases. These phases occur when extended objects, called ''string-nets,'' become highly fluctuating and condense. We construct a large class of exactly soluble 2D spin Hamiltonians whose ground states are string-net condensed. Each ground state corresponds to a different parity invariant topological phase. The models reveal the mathematical framework underlying topological phases: tensor category theory. One of the Hamiltonians--a spin-1/2 system on the honeycomb lattice--is a simple theoretical realization of a universal fault tolerant quantum computer. The higher dimensional case also yields an interesting result: we find that 3D string-net condensation naturally gives rise to both emergent gauge bosons and emergent fermions. Thus, string-net condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions.
- OSTI ID:
- 20665066
- Journal Information:
- Physical Review. B, Condensed Matter and Materials Physics, Vol. 71, Issue 4; Other Information: DOI: 10.1103/PhysRevB.71.045110; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1098-0121
- Country of Publication:
- United States
- Language:
- English
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