Majorana dimer




In solid state physics and quantum many-body physics, and specifically in the context of topological phases of matter, by a Majorana dimer one means a dimer aba \to b (an edge in some graph) that is labeled by an entangled state ψ ab\psi_{a b} of two qbits (“spins”) characterized by the equation

(γ a+ip abγ b)|ψ=0, \big( \gamma_a + i p_{a b} \gamma_b \big) \left\vert \psi \right\rangle \;=\; 0 \,,


(e.g. JGPE 19, III.A)


The notion is due to:

  • Brayden Ware, Jun Ho Son, Meng Cheng, Ryan V. Mishmash, Jason Alicea, and Bela Bauer, Ising anyons in frustration-free Majorana-dimer models, Phys. Rev. B 94, 115127 2016 (arXiv:10.1103/PhysRevB.94.115127)

  • Nicolas Tarantino and Lukasz Fidkowski, Discrete spin structures and commuting projector models for two-dimensional fermionic symmetry-protected topological phases, Phys. Rev. B 94, 115115 2016 (doi:10.1103/PhysRevB.94.115115)

Majorana dimer states are used (not under that name though) for discussion of the SYK model and its AdS2/CFT1 dual in:

Application of Majorana dimers to quantum error correcting codes and holographic entanglement entropy in the Majorana dimer code:

Last revised on May 5, 2021 at 12:41:28. See the history of this page for a list of all contributions to it.