Stringnet condensation: A physical mechanism for topological phases
Abstract
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 “stringnets,” become highly fluctuating and condense. We construct a large class of exactly soluble 2D spin Hamiltonians whose ground states are stringnet 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 stringnet condensation naturally gives rise to both emergent gauge bosons and emergent fermions. Thus, stringnet condensation provides a mechanism for unifying gauge bosons and fermions in 3 and higher dimensions.
 Publication:

Physical Review B
 Pub Date:
 January 2005
 DOI:
 10.1103/PhysRevB.71.045110
 arXiv:
 arXiv:condmat/0404617
 Bibcode:
 2005PhRvB..71d5110L
 Keywords:

 71.10.w;
 11.15.q;
 Theories and models of manyelectron systems;
 Gauge field theories;
 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 High Energy Physics  Theory
 EPrint:
 21 pages, RevTeX4, 19 figures. Homepage http://dao.mit.edu/~wen