Fractionalization in an easy-axis Kagome antiferromagnet

By L. Balents, Matthew Fisher, Steven M. Girvin. 2001

204 citations recorded by the source corpus.

We study an antiferromagnetic spin-$1/2$ model with up to third nearest-neighbor couplings on the Kagome lattice in the easy-axis limit, and show that its low-energy dynamics are governed by a four-site $\mathrm{XY}$ ring exchange Hamiltonian. Simple ``vortex pairing'' arguments suggest that the model sustains a novel fractionalized phase, which we confirm by exactly solving a modification of the Hamiltonian including a further four-site interaction.In this limit, the system is a featureless ``spin liquid,'' with gaps to all excitations, in particular: deconfined ${S}^{z}=1/2$ bosonic ``spinons'' and Ising vortices or ``visons.'' We use an Ising duality transformation to express vison correlators as nonlocal strings in terms of the spin operators, and calculate the string correlators using the ground state wave function of the modified Hamiltonian. Remarkably, this wave function is exactly given by a kind of Gutzwiller projection of an $\mathrm{XY}$ ferromagnet.Finally, we show that the deconfined spin-liquid state persists over a finite range as the additional four-spin interaction is reduced, and study the effect of this reduction on the dynamics of spinons and visons.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/817234b88d727e885ff22f0ddbd84fbb89221e1e

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In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

Citations in the corpus

Lattice gauge theory simulations in the quantum information era (2016, background): “to the same hexagonal plaquette, thus realising the socalled Balents–Fisher–Girvin model [146].”
Prediction of Toric Code Topological Order from Rydberg Blockade (2020, background): “Unfortunately, despite several decades of theoretical and experimental effort [4, 23, 27–31], no clearcut realization of Z2 topological order has been obtained to date.”
Topological entanglement entropy of a Bose-Hubbard spin liquid (2011, methodology): “One important step in this direction occurred with the introduction of a kagome Bose-Hubbard model by Balents, Girvin and Fisher [6].”
Three-body interactions with cold polar molecules (2007, unknown): “The characteristic energy scale W0 = γ2DR 6 0 /a 6 is discussed following equation (6).”
Doping a Mott insulator: Physics of high-temperature superconductivity (2004, methodology): “More exactly soluble or quasi-exactly soluble models were find for dimmer model (Moessner and Sondhi, 2001), spin-1/2 model on Kagome lattice (Balents et al., 2002), boson model on square lattice (Senthil and 7 The Z2 state obtained in Read and Sachdev, 1991 breaks the 90◦ rotation symmetry while…”