Jaideep Mulherkar et al J. Stat. Mech. (2008) P01016 doi:10.1088/1742-5468/2008/01/P01016
Jaideep Mulherkar1, Bruno Nachtergaele1, Robert Sims1 and Shannon Starr2
Show affiliationsWe 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.
E-print Number: 0709.1733
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Refers: to
75.10.Jm Quantized spin models
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
82B10 Quantum equilibrium statistical mechanics (general)
15A18 Eigenvalues, singular values, and eigenvectors
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
Issue 01 (January 2008)
Received 24 September 2007, accepted for publication 20 December 2007
Published 18 January 2008
Jaideep Mulherkar et al J. Stat. Mech. (2008) P01016
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