2000/11/15 by Roderich Moessner, R. Moessner, S. L. Sondhi · 8 citations
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Frustration #Heisenberg model #Hexagonal lattice #Ising model #Mathematics #Monte Carlo method #Phase (matter) #Phase diagram #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum fluctuation #Quantum mechanics #Theoretical and Computational Physics #Valence bond theory #cond-mat.dis-nn #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.63.224401
published as Phys. Rev. B 63, 224401 (2001) · 21 pages latex; 20 figures automatically included
arxiv created 2000/11/15 · openalex publication_date 2001/05/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 kagom'e 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 (kagom'e). We also discuss the effect of finite temperature, as well as the interplay between longitudinal and transverse fields---in the kagom'e 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.