Ising models of quantum frustration - art. no. 224401

We report on a systematic study of two-dimensional, periodic, frustrated Is ing models with quantum dynamics introduced via a transverse magnetic field . The systems studied are the triangular and kagome lattice antiferromagnet s, fully frustrated models on the square and hexagonal (honeycomb) lattices , a planar analog of the pyrochlore antiferromagnet, a pentagonal lattice a ntiferromagnet. as well as two quasi-one-dimensional lattices that have con siderable 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 Landau-Ginzburg-Wilson approach from large fields, as well as quantum Monte Carlo simulations utilizing a clust er algorithm. Our results include instances of quantum order arising from c lassical criticality (triangular lattice) or classical disorder (pentagonal and probably hexagonal) as well as notable instances of quantum disorder a rising from classical disorder (kagome). We also discuss the effect of fini te temperature, as well as the interplay between longitudinal and transvers e fields-in the kagome problem the latter gives rise to a nontrivial phase diagram with bond-ordered and bond-critical phases in addition to the disor dered phase. We also note connections to quantum-dimer models and thereby t o the physics of Heisenberg antiferromagnets in short-ranged resonating val ence-bond phases that have been invoked in discussions of high-temperature superconductivity.