The possibility of gapless excitations in antiferromagnetic spin chains with long-range interactions

2002/05/31 by Tigran Hakobyan
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat

paper · pdf · doi:10.1088/0305-4470/36/47/l01

published as J. Phys. A: Math. Gen. 36 (2003) L599-L604 · 3 pages, RevTeX4

arxiv created 2002/07/24 · openalex publication_date 2003/11/11 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The Lieb–Shultz–Mattis theorem is extended to Heisenberg chains with long-range interactions. We prove that the half-integer spin chain has no gap, if it possesses unique ground state and the exchange decays faster than the inverse-square of distance between spins. The results can be extended to a wide class of one-dimensional models.

Citations

• On Next-Nearest-Neighbor Interaction in Linear Chain. I
• Lattice twist operators and vertex operators in sine-Gordon theory in one dimension
• Topological Approach to Luttinger's Theorem and the Fermi Surface of a Kondo Lattice
• Order Parameter to Characterize Valence-Bond-Solid States in Quantum Spin Chains
• Two soluble models of an antiferromagnetic chain
• Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model