Anomalous non-Abelian statistics for non-Hermitian generalization of Majorana zero modes

In condensed matter physics, non-Abelian statistics for Majorana zero modes (or Fermions) is very important, really exotic, and completely robust. The race searching verifying the corresponding becomes an important frontier in physics. this letter, we generalize to non-Hermitian (NH) topological systems that show universal but quite different properties from their Hermitian counterparts. Based on NH modes, orthogonal nonlocal qubits are well defined. particular, due particle-hole-symmetry breaking, have irrational with continuously tunable braiding Berry phase pi/8 3pi/8. This usual fixed pi/4 example of "irrational phenomenon". one-dimensional Kitaev model taken as numerically verify two modes. numerical results exactly consistent theoretical prediction. With help these gate can be reached thus quantum computation possible.