Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2004-04-26
Phys.Rev. B71 (2005) 045110
Physics
Condensed Matter
Strongly Correlated Electrons
21 pages, RevTeX4, 19 figures. Homepage http://dao.mit.edu/~wen
Scientific paper
10.1103/PhysRevB.71.045110
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 the extended objects, called ``string-nets'', become highly fluctuating and condense. We derive exactly soluble Hamiltonians for 2D local bosonic models whose ground states are string-net condensed states. Those ground states correspond to 2D parity invariant topological phases. These 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 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.
Levin Michael A.
Wen Xiao Gang
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