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This is a collection of lecture notes from three lectures given by Alexei Kitaev at the 2008 Les Houches summer school "Exact methods in low-dimensional physics and quantum computing." They provide a pedagogical introduction to topological phenomena in 1-D superconductors and in the 2-D topological phases of the toric code and honeycomb model.
Phase diagrams of lattice gauge theories with higgs fields
Fradkin, E. and Shenker, S. H. (1979) · 1979
Earlier work this paper cites.
Statistics of the excitations of the resonating-valence-bond state
Read, N. and Chakraborty, B. (1989) · 1989
Earlier work this paper cites.
Flux phase of the half-filled band
Lieb, E. H. (1994) · 1994
Earlier work this paper cites.
Fractional statistics on a torus
Einarsson, T. (1990) · 1998
Earlier work this paper cites.
Unpaired majorana fermions in quantum wires
Kitaev, A. (2000) · 2000
Cited alongside, same era.
Fault-tolerant quantum computation by anyons
Kitaev, A. (2003) · 2003
Cited alongside, same era.
Quasiadiabatic continuation of quantum states: The stability of topological ground-state degeneracy and emergent gauge invariance
Hastings, M. B. and Wen, X. G. (2005) · 2005
Cited alongside, same era.
Anyons in an exactly solved model and beyond
Kitaev, A. (2006) · 2006
Later among the works it cites.
Exact chiral spin liquid with non-abelian anyons
Yao, H. and Kivelson, S. A. (2007) · 2007
Later among the works it cites.
Topological multicritical point in the toric code and 3d gauge higgs models
Tupitsyn, I. S., Kitaev, A., Prokof’ev, N. V., and Stamp, P. C. E. (2008) · 2008
Later among the works it cites.
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