The one-dimensional ANNNI model in a transverse field: analytic and numerical study of effective Hamiltonians
Abstract
We consider a spin-$\frac{1}{2}$ chain with competing nearest and next-nearest neighbor interactions within a transverse magnetic field, which is known to be an equiavelent to the ANNNI model. When studing thermodynamics of the 2D ANNNI model Villain and Bak arrived to a free fermion approximation that neglects heavy excitations from the ferromagnetic ground state, which is an appropriate description close to the paramagnetic-ferromagnetic transition. In the vicinity of the floating-phase/anti-phase transition another sort of quasiparticles, but free fermions too, appears to be convenient. Although free fermions are a suitable tool for investigation of the phase diagram and the critical properties, they are defined on the fictitious lattice which makes the analysis non-rigorous. Here we deal with a proper fermion scheme which is especially effective %devised to describe the floating-phase/anti-phase transition. for performing exact diagonalization calculations for cyclic chains. Systems up to size $L=32$ has been analysed and the predictions of the effective fermion Hamiltonian has been confirmed. Various predictions for the infinite system and the critical properties are derived.
- Publication:
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Zeitschrift fur Physik B Condensed Matter
- Pub Date:
- November 1996
- DOI:
- 10.1007/s002570050252
- arXiv:
- arXiv:cond-mat/9604051
- Bibcode:
- 1996ZPhyB.101..597R
- Keywords:
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- Condensed Matter
- E-Print:
- 30 RevTeX pages, 10 postscript figures