Michael Karbach et al 2008 J. Phys. A: Math. Theor. 41 205002 doi:10.1088/1751-8113/41/20/205002
Interaction and thermodynamics of spinons in the XX chain
Michael Karbach1,2, Gerhard Müller2 and Klaus Wiele1,2
Show affiliationsThe mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) for finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N → ∞ the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane–Shastry model.
- PACS
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75.10.Jm Quantized spin models
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
- MSC
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82B30 Statistical thermodynamics (See also 80-XX)
82B23 Exactly solvable models; Bethe ansatz
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
- Subjects
- Dates
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Issue 20 (23 May 2008)
Received 3 March 2008
Published 23 April 2008
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Interaction and thermodynamics of spinons in the XX chain
Michael Karbach et al 2008 J. Phys. A: Math. Theor. 41 205002
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