| Summary: | We study the open XXZ spin chain in the anti-ferromagnetic regime and for
generic longitudinal magnetic fields at the two boundaries. We discuss the
ground state via the Bethe ansatz and we show that, for a chain of even length
L and in a regime where both boundary magnetic fields are equal and bounded by
a critical field, the spectrum is gapped and the ground state is doubly
degenerate up to exponentially small corrections in L. We connect this
degeneracy to the presence of a boundary root, namely an excitation localized
at one of the two boundaries. We compute the local magnetization at the left
edge of the chain and we show that, due to the existence of a boundary root,
this depends also on the value of the field at the opposite edge, even in the
half-infinite chain limit. Moreover we give an exact expression for the large
time limit of the spin autocorrelation at the boundary, which we explicitly
compute in terms of the form factor between the two quasi-degenerate ground
states. This, as we show, turns out to be equal to the contribution of the
boundary root to the local magnetization. We finally discuss the case of chains
of odd length.
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