Vionnet, GrégoireKumar, BrijeshMila, Frédéric2019-06-192019-06-192019-06-19201710.1103/PhysRevB.95.174404https://infoscience.epfl.ch/handle/20.500.14299/158313We study the effect of antiferromagnetic longitudinal coupling on the one-dimensional transverse field Ising model with nearest-neighbor couplings. In the topological phase where, in the thermodynamic limit, the ground state is twofold degenerate, we show that, for a finite system of N sites, the longitudinal coupling induces N level crossings between the two lowest-lying states as a function of the field. We also provide strong arguments suggesting that these N level crossings all appear simultaneously as soon as the longitudinal coupling is switched on. This conclusion is based on perturbation theory and a mapping of the problem onto the open Kitaev chain, for which we write down the complete solution in terms of Majorana fermions.text::journal::journal article::research article