Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer

• URL: http://arxiv.org/abs/2010.05982v1
• Date: Mon, 12 Oct 2020 19:16:36 GMT
• Title: Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Authors: R. Wiedmann, L. Lenke, M.R. Walther, M. M\"uhlhauser, K.P. Schmidt
• Abstract summary: We show that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled $mathbbZtimesmathbbZ$ and the strongly-coupled $mathbbZ$ can be described by the condensation of bosonic quasiparticles from both sides.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We demonstrate that two toric code layers on the square lattice coupled by an Ising interaction display two distinct phases with intrinsic topological order. The second-order quantum phase transition between the weakly-coupled $\mathbb{Z}_2\times\mathbb{Z}_2$ and the strongly-coupled $\mathbb{Z}_2$ topological order can be described by the condensation of bosonic quasiparticles from both sides and belongs to the 3d Ising$^*$ universality class. This can be shown by an exact duality transformation to the transverse-field Ising model on the square lattice, which builds on the existence of an extensive number of local $\mathbb{Z}_2$ conserved parities. These conserved quantities correspond to the product of two adjacent star operators on different layers. Notably, we show that the low-energy effective model derived about the limit of large Ising coupling is given by an effective single-layer toric code in terms of the conserved quantities of the Ising toric code bilayer. The two topological phases are further characterized by the topological entanglement entropy which serves as a non-local order parameter.

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