A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state

Thomas G Kennedy, Elliott H. Lieb, Hal Tasaki

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Abstract

We continue the study of valence-bond solid antiferromagnetic quantum Hamiltonians. These Hamiltonians are invariant under rotations in spin space. We prove that a particular two-dimensional model from this class (the spin-3/2 model on the hexagonal lattice) has a unique ground state in the infinite-volume limit and hence no Néel order. Moreover, all truncated correlation functions decay exponentially in this ground state. We also characterize all the finite-volume ground states of these models (in every dimension), and prove that the two-point correlation function of the spin-2 square lattice model with periodic boundary conditions has exponential decay.

Original languageEnglish (US)
Pages (from-to)383-415
Number of pages33
JournalJournal of Statistical Physics
Volume53
Issue number1-2
DOIs
Publication statusPublished - Oct 1988
Externally publishedYes

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Keywords

  • Néel order
  • Quantum antiferromagnet

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

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