Level crossings induced by a longitudinal coupling in the transverse field Ising chain

Abstract

We study the effect of antiferromagnetic longitudinal coupling on the one-dimensional transverse field Ising model with nearest-neighbour 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.

9 pages, 11 figures; v2: minor changes

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• Statistics tuned entanglement of the boundary modes in coupled Su-Schrieffer-Heeger chains
• Exact zero modes in frustrated Haldane chains
• Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
• Effect of interaction on the Majorana zero modes in the Kitaev chain at half filling
• Rigorous decoupling between edge states in frustrated spin chains and ladders
• Unification of Finite Symmetries in Simulation of Many-body Systems on Quantum Computers
• Perturbative approach to quantum tunneling and quantum interferences in spin clusters