Strong zero modes and edge states in the interacting fermion chain without pairing

The operator of the strong zero mode for the one-dimensional system of interacting fermions without pairing is presented. It is conjectured that the strong zero mode is related to the Majorana edge eigenstate, which is shown to exist (using the exact Bethe ansatz study) in this system. The results are robust with respect to the sign randomness of hopping amplitudes (and if the pairing amplitudes are nonzero, similar results exist for equal sign randomness of hopping and pairing amplitudes).