FIZIKA B 8 (1999) 3, 453-468

ON BETHE STRINGS IN THE TWO-PARTICLE SECTOR OF THE CLOSED SU(2)_Q INVARIANT SPIN CHAIN

AMON ILAKOVAC, MARKO KOLANOVIĆ, SILVIO PALLUA and PREDRAG PRESTER

Department of Theoretical Physics, University of Zagreb,
Bijenička c. 32, 10000 Zagreb, Croatia
E-mail addresses: [email protected],    [email protected],    [email protected],    [email protected]

Received 4 March 1999; Accepted 26 April 1999

In this paper we investigate complex solutions of the Bethe equations in the two-particle 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 highest-weight Bethe states.

PACS numbers: 11.10.Kk, 75.10.Jm, 11.15.Tk
UDC 539.126

Keywords: two-particle sector, arbitrary finite number of sites, thermodynamic limit, Bethe equations, number of complex solutions (strings), position in the spectrum, crossing of levels, connection to the ground state and transformation to the real solutions, number of highest-weight Bethe states

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