Phys. Rev. Lett. 89, 077204 (2002) [4 pages]Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin ChainsReceived 20 December 2001; published 30 July 2002 We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte Carlo method. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.89.077204
DOI:
10.1103/PhysRevLett.89.077204
PACS:
75.10.Jm, 75.40.Cx
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