Ising models of quantum frustration

Abstract

We report on a systematic study of two dimensional, periodic, frustrated Ising models with a quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular and kagome 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 a 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 (LGW) 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). We also discuss the effect of a finite temperature, as well as the interplay between longitudinal and transverse fields-in the kagome problem the latter gives rise to a non-trivial 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.

Singular or non-Fermi liquids

“…Then defects in this state due to deviation from half-ÿlling can plausibly support excitations which are charged spinless bosons. Further work on this idea may be found in [225,188]. Related ideas were put forth in [82,236].…”

“…Several variants of these ideas have been proposed with and without attempts to suppress the unphysical condensation through uctuations [188]. The trouble is that such uctuations tend to bind the spinons and holons and the happy situation in one dimension where they exist independently-being protected by (extra) conservation laws, see Section 4.9-is hard to realize.…”

Detecting nonmagnetic excitations in quantum magnets

“…These are projective symmetry operations. On triangular lattice, they were first studied by Moessner and Sondi [29]. We follow their convention.…”

“…The visons are non-local excitations; singlet density fluctuations involves at least two visons [8,9]. Vison-dispersion can be determined by Z 2 gauge theory [1,29]. The coupling between one phonon and two visons induces new phonon modes below the edge of two-vison continuum.…”

“…It possesses topological order [1]: the degree of degeneracy of ground state depends on the topology of the hosting manifold. The low energy theory is the Z 2 gauge theory [1,29]. Elementary excitations are visons [6,7], massive bosonic particles.…”