1996 # Onset of incommensurability at the valence-bond-solid point in the*S*=1 quantum spin chain

**Abstract:** Most of the present understanding of the Sϭ1 quantum spin chains displaying the Haldane gap is coming from the so-called valence-bond-solid ͑VBS͒ Hamiltonian which has an exactly known ground state. We show that this point is characterized by the onset of short-range incommensurate spin correlations in the oneparameter family of Hamiltonians H ϭcos͚ i S i •S iϩ1 ϩsin͚ i (S i •S iϩ1 ) 2 . This gives a physical meaning to this special point. We establish precise values for the gaps, correlations, the string orde…

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(204 citation statements)

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“…This is a topological phase, containing for θ = arctan(1/3) the AKLT point 28 whose ground state can be written in terms of matrix product states. The entire phase is characterized by free edge spins and a non vanishing string order parameter 22,29 :…”

confidence: 99%

“…This is a topological phase, containing for θ = arctan(1/3) the AKLT point 28 whose ground state can be written in terms of matrix product states. The entire phase is characterized by free edge spins and a non vanishing string order parameter 22,29 :…”

confidence: 99%

“…Finally, Eq. (7) can be used to realize the most general spin-1 bilinear-biquadratic model 75 with the Y 2,0 angular dependence 69 . It would be particularly interesting to follow Refs.…”

confidence: 99%

“…16) θ AKLT = arctan 1/3, the ground state is exactly known to be a valence bond solid, and for θ > θ AKLT the spin correlation functions become incommensurate. 22,27 Between the ULS point and θ = π/2, the system is gapless and shows antiferroquadrupolar spin-nematic quasi long range order (QLRO). 24 For negative values of θ, between θ = −3/4π and θ = −π/4 the system is dimerized and has a finite gap.…”

confidence: 99%

“…[11][12][13][14][15][16][17][18][19][20][21][22][23][24] For our considerations, it is helpful to keep in mind the following aspects of its phase diagram. Between the two integrable points θ TB = −π/4 (the TakhtajanBabujian point, 14,15 TB) and θ ULS = π/4 (the Uimin-LaiSutherland point, [11][12][13] ULS) the chain possesses a finite Haldane gap.…”

confidence: 99%