Journal of Physics Conference Series

Singlet ground states of the bilinear-biquadratic exchange Hamiltonian with reflection symmetry

Kengo Tanaka

Published Sep 28, 2011• 0 citations

Abstract

We apply the Lieb–Schupp method to the isotropic spin- S Hamiltonian with bilinear (− J / S 2 ) and biquadratic (− J '/ S 4 ) exchange interactions on finite lattices with reflection-symmetry to prove that finite volume ground states of the models are spin singlet in the parameter region J ' ≥ 2 S 2 J , J ' ≥ 0.

DOI: 10.1088/1742-6596/320/1/012008

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Journal of Physics Conference Series

Singlet ground states of the bilinear-biquadratic exchange Hamiltonian with reflection symmetry

Kengo Tanaka

Published Sep 28, 2011• 0 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/320/1/012008

Related papers

Singlet ground state of the bilinear-biquadratic exchange Hamiltonian

Akinori Tanaka, Toshihiro Idogaki

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{S}_{\mathrm{tot}}

of the lowest-energy state in each subspace classified by

M,

an eigenvalue of

z

component of the total spin, depends on the parity of

M,

i.e.,

{S}_{\mathrm{tot}}=|M|

for even

M

and

{S}_{\mathrm{tot}}=|M|+1

for odd

M

on an even number site lattice and vice versa on an odd number site lattice.

S

. The sufficient conditions for the existence of ferromagnetic ground state are also found exactly. The approximate quantum phase diagrams are presented using the exact results, together with a variational estimate for the N\'eel antiferromagnetic phase. A two-leg spin-

1∕2

ladder model, based on one of the above constructions, is considered which admits exact solution for a large number of eigenstates. The ladder model is shown to have exact level crossing between the rung-singlet state and the AKLT state in the singlet ground state. Also introduced is the notion of perpendicularity for quantum spin vectors, which appears in the discussion on one of the two checkerboard models, and is discussed in the Appendix.