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Low Temperature Physics

Boundary bound states in the Bose–Hubbard-like chain

Andrei A. Zvyagin

Published May 1, 2007• 2 citations
Publisher

Abstract

The degenerate Hubbard-like chain with open boundary conditions is studied with the help of the Bethe ansatz. The special case of the Bose–Hubbard-like chain is studied in detail. Boundary bound states, which appear as a consequence of local potential(s) applied to the edge(s) of the open chain, are studied in the ground state.
DOI
10.1063/1.2737558

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Using the Bethe ansatz we study the spectrum of boundary bound states of the SU ( N ) generalization of the one-dimensional Hubbard model with open boundaries and applied boundary potentials. The number of electrons bound by the boundary field is found from the surface contribution to the energy. Finite size corrections to the low-lying energies in this system and use of the predictions of boundary conformal field theory allows us to study the exponents related to the orthogonality catastrophe and absorption edges.
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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.