2020/10/12 by Raymond Wiedmann, R. Wiedmann, Lea Lenke +7 · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Ising model #Lattice (music) #Mathematical physics #Phase transition #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Theoretical and Computational Physics #Topological order #Toric code #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.102.214422
published as Phys. Rev. B 102, 214422 (2020) · 6 pages, 3 figures
arxiv created 2020/10/12 · openalex publication_date 2020/12/17 · arxiv updated 2021/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 ℤ2\ifmmode×\else\texttimes\fiℤ2 and the strongly coupled ℤ2 topological order can be described by the condensation of bosonic quasiparticles from both sides and belongs to the three-dimensional 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 ℤ2 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 nonlocal order parameter.