Ising models of quantum frustration

Journal Article · Fri Jun 01 04:00:00 EDT 2001 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.63.224401· OSTI ID:40203453

Moessner, R; Sondhi, S L

We report on a systematic study of two-dimensional, periodic, frustrated Ising models with quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular and kagome{prime} 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 quasi-one-dimensional 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 Landau-Ginzburg-Wilson 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 (kagome{prime}). We also discuss the effect of finite temperature, as well as the interplay between longitudinal and transverse fields{emdash}in the kagome{prime} problem the latter gives rise to a nontrivial phase diagram with bond-ordered and bond-critical phases in addition to the disordered phase. We also note connections to quantum-dimer models and thereby to the physics of Heisenberg antiferromagnets in short-ranged resonating valence-bond phases that have been invoked in discussions of high-temperature superconductivity.

• Sponsoring Organization: (US)
• OSTI ID: 40203453
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 22 Vol. 63; ISSN 0163-1829
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
CRITICALITY
ISING MODEL
MAGNETIC FIELDS
PHASE DIAGRAMS
PHYSICS
PYROCHLORE
SUPERCONDUCTIVITY
VARIATIONAL METHODS