Planar pyrochlore, quantum ice and sliding ice

R. Moessner, Oleg Tchernyshyov, Shivaji Lal Sondhi

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41 Scopus citations


We study quantum antiferromagnetism on the highly frustrated planar pyrochlore lattice, also known as the square lattice with crossings. The quantum Heisenberg antiferromagnet on this lattice is of interest as a two-dimensional analogue of the pyrochlore lattice magnet. By combining several approaches we conclude that this system is most likely ordered for all values of spin, S, with a two-fold degenerate valence-bond solid being the ground state for small S. We show next that the Ising antiferromagnet with a weak four-spin exchange, equivalent to square ice with the leading quantum dynamics, exhibits analogous plaquette order. As a byproduct of this analysis we obtain, in the system of weakly coupled ice planes, a sliding phase with XY symmetry; at intermediate couplings, long range "anti-ferroelectric" order is stabilized.

Original languageEnglish (US)
Pages (from-to)755-772
Number of pages18
JournalJournal of Statistical Physics
Issue number1-4
StatePublished - Aug 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • frustration
  • ice
  • quantum magnetism
  • sliding phase


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