

FIZIKA B 8 (1999) 3, 453468 ON BETHE STRINGS IN THE TWOPARTICLE SECTOR OF THE CLOSED SU(2)_{Q} INVARIANT SPIN CHAINAMON ILAKOVAC, MARKO KOLANOVIĆ, SILVIO PALLUA and PREDRAG PRESTER Department of Theoretical Physics, University of Zagreb, Received 4 March 1999; Accepted 26 April 1999In this paper we investigate complex solutions of the Bethe equations in the
twoparticle sector, both for arbitrary finite number of sites and for the thermodynamic
limit. We find the number of complex solutions (strings) and compare it with the string
conjecture prediction. Some simple properties of these solutions like position in the
spectrum, crossing of levels, connection to the ground state and transformation to the
real solutions are discussed. Counting both real and complex solutions, we find expected
number of highestweight Bethe states. PACS numbers: 11.10.Kk, 75.10.Jm, 11.15.Tk

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