Isolated eigenvalues of the ferromagnetic spin-J XXZ chain with kink boundary
conditions

doi:10.1088/1742-5468/2008/01/P01016

Isolated eigenvalues of the ferromagnetic spin-J XXZ chain with kink boundary conditions

Jaideep Mulherkar et al J. Stat. Mech. (2008) P01016 doi: 10.1088/1742-5468/2008/01/P01016

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Jaideep Mulherkar¹, Bruno Nachtergaele¹, Robert Sims¹ and Shannon Starr²
¹ Department of Mathematics, University of California, Davis, CA 95616-8633, USA
² Department of Mathematics, University of Rochester, Rochester, NY 14627, USA
E-mail: jmulherkar@math.ucdavis.edu, bxn@math.ucdavis.edu, rjsims@math.ucdavis.edu and sstarr@math.rochester.edu

Abstract. We investigate the low-lying excited states of the spin J ferromagnetic XXZ chain with Ising anisotropy Δ and kink boundary conditions. Since the third component of the total magnetization, M, is conserved, it is meaningful to study the spectrum for each fixed value of M. We prove that for J≥3/2 the lowest excited eigenvalues are separated by a gap from the rest of the spectrum, uniformly in the length of the chain. In the thermodynamic limit, this means that there are a positive number of excitations above the ground state and below the essential spectrum.

Key words: rigorous results in statistical mechanics; spin chains, ladders and planes (theory)

E-print number: 0709.1733
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Received 24 September 2007, accepted for publication 20 December 2007
Published 18 January 2008

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Isolated eigenvalues of the ferromagnetic spin-J XXZ chain with kink boundary conditions

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