Ising models of quantum frustration
Abstract
We report on a systematic study of twodimensional, periodic, frustrated Ising models with quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular and kagomé lattice antiferromagnets, fully frustrated models on the square and hexagonal (honeycomb) lattices, a planar analog of the pyrochlore antiferromagnet, a pentagonal lattice antiferromagnet, as well as two quasionedimensional lattices that have considerable pedagogical value. All of these exhibit a macroscopic degeneracy at T=0 in the absence of the transverse field, which enters as a singular perturbation. We analyze these systems with a combination of a variational method at weak fields, a perturbative LandauGinzburgWilson approach from large fields, as well as quantum Monte Carlo simulations utilizing a cluster algorithm. Our results include instances of quantum order arising from classical criticality (triangular lattice) or classical disorder (pentagonal and probably hexagonal) as well as notable instances of quantum disorder arising from classical disorder (kagomé). We also discuss the effect of finite temperature, as well as the interplay between longitudinal and transverse fieldsin the kagomé problem the latter gives rise to a nontrivial phase diagram with bondordered and bondcritical phases in addition to the disordered phase. We also note connections to quantumdimer models and thereby to the physics of Heisenberg antiferromagnets in shortranged resonating valencebond phases that have been invoked in discussions of hightemperature superconductivity.
 Publication:

Physical Review B
 Pub Date:
 June 2001
 DOI:
 10.1103/PhysRevB.63.224401
 arXiv:
 arXiv:condmat/0011250
 Bibcode:
 2001PhRvB..63v4401M
 Keywords:

 75.10.b;
 05.50.+q;
 75.10.Jm;
 75.30.Kz;
 General theory and models of magnetic ordering;
 Lattice theory and statistics;
 Quantized spin models;
 Magnetic phase boundaries;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 21 pages latex