Physical Meaning of the Affleck-Kennedy-Lieb-Tasaki S=1 Quantum spin chain

Abstract

Most of the present understanding of the S=1 quantum spin chains displaying the Haldane gap is coming from the so-called valence-bond-solid 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 one-parameter family of Hamiltonians with biquadratic coupling: H = sum_i S_i S_{i+1} +alpha sum_i ( S_i S_{i+1} )^2. This gives a physical meaning to this special point. We establish precise values for the gaps, correlations, the string order parameter, and identify the VBS point as a *disorder* point in the sense of classical statistical mechanics. It is a quantum remnant of the classical transition between a ground state with long-range Néel order and a ground state with incommensurate long-range order.

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References in corpus (3)

• Search for the Nondimerized Quantum Nematic Phase in the Spin-1 Chain
• Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
• Solitonic excitations in the Haldane phase of a S=1 chain

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