A symmetry principle for Topological Quantum Order

Details A symmetry principle for Topological Quantum Order A symmetry principle for Topological Quantum Order

2007-02-16

arxiv.org/abs/cond-mat/0702377v5

Physics

Condensed Matter

Strongly Correlated Electrons

57 pages, 14 figures, references added

Scientific paper

10.1016/j.aop.2008.11.002

We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The guiding principle behind our approach is that of symmetries and entanglement. We introduce the concept of low-dimensional Gauge-Like Symmetries (GLSs), and the physical conservation laws (including topological terms and fractionalization) which emerge from them. We prove then sufficient conditions for TQO at both zero and finite temperatures. The topological defects which are associated with the restoration of GLSs lead to TQO. Selection rules associated with the GLSs enable us to systematically construct states with TQO; these selection rules do not rely on the existence of a finite gap between the ground states to all other excited states. All currently known examples of TQO display GLSs. We analyze spectral structures and show that Kitaev's toric code model and Wen's plaquette model are equivalent and reduce, by a duality mapping, to an Ising chain. Despite the spectral gap in these systems, the toric operator expectation values may vanish once thermal fluctuations are present. This mapping illustrates that the quantum states themselves in a particular (operator language) representation encode TQO and that the duality mappings, being non-local in the original representation, disentangle the order. We present a general algorithm for the construction of long-range string orders in general systems with entangled ground states.

Affiliated with

Also associated with

No associations

Rating

A symmetry principle for Topological Quantum Order does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A symmetry principle for Topological Quantum Order, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A symmetry principle for Topological Quantum Order will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-196150