Geometric entanglement in Kitaev's toric code and transition to trivial phase by string tension

Speaker: 
Tzu-Chieh Wei, Stony Brook
Event Date and Time: 
Mon, 2014-07-28 15:00 - 16:00
Location: 
Hennings 301
Local Contact: 
Robert Raussendorf
Intended Audience: 
Graduate
I will introduce a geometric measure of entanglement to quantify entanglement in toric code ground states. It turns out that the geometric entanglement exhibits a bulk law and an additional constant, the latter being the same as the topological entanglement entropy. A string tension can be applied to frustrate large loop configuration in the toric code ground state, and when the tension is sufficiently large, the wavefunction becomes a trivial product state. Somewhere in between the exact toric code ground state and the trivial product state, there must exist a phase transition. I will present our results to extract the "topological" part of the geometric entanglement as the string tension varies and demonstrate that it identifies the correct transition point. I will also discuss the possibility of using the geometric entanglement to identify the so-called minimally entropy states, and thus the modular matrices of topological models (toric code and beyond).
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