Ising models of quantum frustration

By Roderich Moessner, Shiv Sondhi. 2000

271 citations recorded by the source corpus.

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 therebymore » to the physics of Heisenberg antiferromagnets in short-ranged resonating valence-bond phases that have been invoked in discussions of high-temperature superconductivity.« less

Subfields: Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/b87c453eb4b8b9114f953cc0384ef00ce6bdc9b9

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Citations in the corpus

Valence Bonds in Random Quantum Magnets: Theory and Application to YbMgGaO4 (2017, background): “1 but also the known [85,86,88] plaquette-VBS phases, whose resonances involve various four-spin, 12-spin, or 16-spin clusters.”
Quantum Simulation of a Lattice Schwinger Model in a Chain of Trapped Ions (2013, background): “As it becomes apparent in the first three terms of HG, the way gauge invariance is recovered in this spin basis is reminiscent of the basic frustration induced by Ising interactions in triangular (ladder) geometries at fixed magnetization [65].”
Singular or Non-Fermi Liquids (2001, background): “del to be localised dimers. Then defects in this state due to deviation from half-ﬁlling can plausibly support excitations which are charged spinless bosons. Further work on this idea may be found in [210,176]. Related ideas were put forth in [80]. These are very attractive set of ideas and no proof”
Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “The model is also relevant to U(1) lattice gauge theory in its quantum link (143) and dimer model (144, 145, 146) formulations, and to the fractional quantum Hall effect at ν = 1/3 in the thin-torus limit (112).”
Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface (2015, background): “This behavior is familiar from “odd” gauge theories [38,39].”
Quantum spin-ice and dimer models with Rydberg atoms (2014, background): “When different initial fillings are considered, one has access to different quantum dynamics: A notable case is the N 1⁄4 L=4 case, which defines a constrained dynamics on a manifold where a single boson sits close to each vertex [10].”
Evidence for quantum annealing with more than one hundred qubits (2013, background): “[41] Moessner, R.”
Observing the Space- and Time-Dependent Growth of Correlations in Dynamically Tuned Synthetic Ising Models with Antiferromagnetic Interactions (2017, background): “The most interesting feature occurs when ħδ=U 1⁄4 z=2, where an “order by disorder” process occurs [37].”