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

TL;DR

This paper clarifies the physical significance of the Affleck-Kennedy-Lieb-Tasaki point in S=1 quantum spin chains by linking it to incommensurate correlations and classical disorder points, enhancing understanding of the Haldane gap.

Contribution

It provides a physical interpretation of the AKLT point as a disorder point related to incommensurate correlations in a family of Hamiltonians.

Findings

Identifies the AKLT point as a disorder point with incommensurate correlations.

Establishes precise values for gaps, correlations, and string order parameter.

Connects the AKLT point to a classical transition between different magnetic orders.

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 N\'eel order and a ground state with incommensurate long-range order.