Valence Bond Entanglement Entropy

2007/03/31 by Fabien Alet, Sylvain Capponi, Nicolas Laflorencie +1
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.99.117204

published as Phys. Rev. Lett. 99, 117204 (2007) · 4 pages, 3 figures, v2: small corrections, published version

openalex publication_date 2007/09/12 · arxiv created 2007/09/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce for SU(2) quantum spin systems the valence bond entanglement entropy as a counting of valence bond spin singlets shared by two subsystems. For a large class of antiferromagnetic systems, it can be calculated in all dimensions with quantum Monte Carlo simulations in the valence bond basis. We show numerically that this quantity displays all features of the von Neumann entanglement entropy for several one-dimensional systems. For two-dimensional Heisenberg models, we find a strict area law for a valence bond solid state and multiplicative logarithmic corrections for the Néel phase.

Citations

• Scaling of Entanglement Entropy in the Random Singlet Phase
• On Next-Nearest-Neighbor Interaction in Linear Chain. I
• Some formal results for the valence bond basis
• Entanglement versus Correlations in Spin Systems
• Entropy and Area
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground-state phase diagram of quantum Heisenberg antiferromagnets on the anisotropic dimerized square lattice