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A quantum topological phase transition at the microscopic level · Around

2007

A quantum topological phase transition at the microscopic level

Castelnovo, C., Chamon, C.

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We study a quantum phase transition between a phase which is topologically ordered and one which is not.

We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling constant that takes the system across the phase transition.
We compute the entanglement and the topological entropy of the system as a function of this coupling constant, and show that the topological entropy remains constant all the way up to the critical point, and jumps to zero beyond it.
Despite the jump in the topological entropy, the transition is second order as detected via any local observable.

Built on

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This condition is actually immaterial, and can be avoided using an approach similar to the one by Furukawa and Misguich [Phys. Rev. B 75
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E. Fradkin, and J. E. Moore, Phys. Rev. Lett. 97

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A similar behavior – i.e., the lack of a local order parameter but display of local non-analyticities – was recently argued by Z. Nussinov and G. Ortiz to characterize as well a temperature-driven topological phase transition in the Kitaev model [arXiv:cond-mat/0702377]

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S. Papanikolaou, K. Raman, and E. Fradkin, Phys. Rev. B 76

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