A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states
M. BrockmannInstitute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090-GL Amsterdam, The NetherlandsJacopo De NardisInstitute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090-GL Amsterdam, The NetherlandsB. WoutersInstitute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090-GL Amsterdam, The NetherlandsJ-S CauxInstitute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, 1090-GL Amsterdam, The Netherlands
2014en
ABI
Abstract
We derive a determinant expression for overlaps of Bethe states of the XXZ spin chain with the N{\'e}el state, the ground state of the system in the antiferromagnetic Ising limit. Our formula, of determinant form, is valid for generic system size. Interestingly, it is remarkably similar to the well-known Gaudin formula for the norm of Bethe states, and to another recently-derived overlap formula appearing in the Lieb-Liniger model.
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Cited by 40 references