2005/08/21 by Roderich Moessner, R. Moessner, S. L. Sondhi +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Degenerate energy levels #Dimer #Ground state #Hamiltonian (control theory) #Ising model #Lattice (music) #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pyrochlore #Quantum #Quantum mechanics #Symmetry breaking #Theoretical and Computational Physics #Theoretical physics #Translational symmetry #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.73.094430
published as Phys. Rev. B 73, 094430 (2006) · 9 pages
arxiv created 2005/08/21 · openalex publication_date 2006/03/22 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study a large-N deformation of the S=1∕2 pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading nontrivial order. In this limit, the ground state manifold---while extensively degenerate---breaks the inversion symmetry of the lattice, which implies a finite temperature Ising transition without translational symmetry breaking. At lower temperatures and further in the 1∕N expansion, we discuss an effective Hamiltonian within the degenerate manifold, which has a transparent physical interpretation as representing dimer potential energies. We find mean-field ground states of the effective Hamiltonian which exhibit translational symmetry breaking. The entire scenario offers a new perspective on previous treatments of the SU(2) problem not controlled by a small parameter, in particular showing that a mean-field state considered previously encodes the physics of a maximally flippable dimer configuration. We also comment on the difficulties of extending our results to the SU(2) case, and note implications for classical dimer models.