  The quantum XX chain - or rather ring - is studied as a toy model of an
interface. Two transverse field patterns are used to define the interface, on
the one hand a staggered field, on the other hand a step-like configuration,
from -h to +h. The interface leads to Friedel oscillations and proximity
effects, in particular close to the quantum phase transition of the bulk, which
is a metal-insulator transition in the fermionic language. The most prominent
interface effects appear for odd-numbered rings, for which - in contrast to
even chains - the ground state is doubly degenerate. In the regime where the
bulk energy spectrum is gapped a level appears close to midgap, with a wave
function localized in the region of the interface. The two members of the
ground state doublet have two different particle number parities and spin
components S_z=+-1/2. They also have different energy levels and thus the
degeneracy does not originate from different occupancies of a rigid band
structure, but rather from a global symmetry. The unitary transformation
linking the two degenerate ground states resembles a Majorana operator.
Coherent superpositions of the two states may be suitable candidates for well
protected qubits.
