Abstract:
We consider a system of interacting spinless fermions on an open chain which, in the absence of interactions, reduces to the celebrated Kitaev/Majorana chain [1]. In the non-interacting case, a signal of topological order is the appearance of zero-energy modes localized near the edges. We show that the exact ground states can be obtained analytically even in the presence of strong repulsive interactions
when the chemical potential is tuned to a particular function of
the other parameters. As with the non-interacting case,
the obtained ground states are two-fold degenerate and differ in fermion parity. We prove that the obtained ground states are adiabatically connected to the ground states of the non-interacting model without gap closing. We also demonstrate explicitly that
there exists a set of operators that intertwine the degenerate
ground states with different fermion parities, and can be thought
of as edge zero modes in the interacting system [2].
[1] A. Yu. Kitaev, Phys.-Usp. 44, 131 (2001), cond-mat/0010440.
[2] H. Katsura, M. Takahashi, and D. Schuricht, in preparation.