https://doi.org/10.1007/s100510050930
Incommensurability in the magnetic excitations of the bilinear-biquadratic spin-1 chain
1
Service de Physique Théorique,
CEA Saclay, 91191 Gif-sur-Yvette, France
2
Laboratoire de Physique Quantique,
IRSAMC, Université Paul Sabatier, 31062 Toulouse Cedex 4, France
Corresponding author: a thierry@spht.saclay.cea.fr
Received:
16
December
1998
Published online: 15 September 1999
We study the magnetic excitation spectrum of the
spin-1 chain with Hamiltonian
.
We focus on the range 
where the spin chain is in the gapped Haldane phase.
The excitation spectrum and static structure factor is
studied using direct Lanczos diagonalization of small systems
and density-matrix renormalization group techniques
combined with the single-mode approximation.
The magnon dispersion has a minimum
at 
until a critical value 
is reached
at which the curvature (velocity) vanishes.
Beyond this point, which is distinct from the VBS point
and the Lifshitz point, the minimum lies at an incommensurate
value that goes smoothly to 
when θ approaches
, the Lai-Sutherland point. The mode
remains isolated from the other states:
there is no evidence of spinon
deconfinement before the point 
.
These findings explain recent observation of the behavior
of the magnetization curve 
for 
.
PACS: 75.10.Jm – Quantized spin models / 75.20.Hr – Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1999
