Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains

2001/12/20 by Masaaki Nakamura, Synge Todo · 5 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.stat-mech #cond-mat.str-el

paper · pdf · doi:10.1103/physrevlett.89.077204

published as Phys. Rev. Lett. 89 (2002) 077204 · 4 pages, 3 figures

arxiv created 2001/12/20 · openalex publication_date 2002/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Two soluble models of an antiferromagnetic chain
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model

Cited by

• The possibility of gapless excitations in antiferromagnetic spin chains with long-range interactions
• Twisted-order parameter applied to dimerized ladders
• Phase diagram of the frustrated spin ladder
• Classical many-particle systems with unique disordered ground states
• Geometric phase and quantum phase transition: Two-band model