Fractionalized excitations in the spin liquid state of a kagom\'{e}
  lattice antiferromagnet

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Abstract

New physics can emerge in magnetic materials where quantum fluctuations are enhanced due to reduced dimensionality and strong frustration. One long sought example is the resonating-valence-bond (RVB) state, where atomic magnetic moments are strongly correlated but do not order or freeze even in the limit of T -> 0. The RVB ground state does not break conventional symmetries, such as lattice translation or spin-rotation. The realization of such a quantum spin liquid in two-dimensions would represent a new state of matter. It is believed that spin liquid physics plays a role in the phenomenon of high-Tc superconductivity, and the topological properties of the spin liquid state may have applications in the field of quantum information. We present neutron scattering measurements of the spin excitations on single crystal samples of the spin-1/2 kagom\'{e} lattice antiferromagnet ZnCu3(OD)6Cl2 (also called herbertsmithite). Our observation of a spinon continuum in a two-dimensional magnet is remarkable first. The results serve as a key fingerprint of the quantum spin liquid state in herbertsmithite.

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Topology of the resonating valence-bond state: Solitons and high-Tcsuperconductivity

Steven Kivelson, Daniel S. Rokhsar, James Sethna (1987)

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Spin Liquid Ground State of the \(S=1/2\) Kagome Heisenberg Model

Simeng Yan, Steven R. White, David Huse (2010)

Condensed matter physicists have long sought a realistic two-dimensional (2D) magnetic system whose ground state is a {\it spin liquid}---a zero temperature state in which quantum fluctuations have melted away any form of magnetic order. The nearest-neighbor \(S=1/2\) Heisenberg model on the kagome lattice has seemed an ideal candidate, but in recent years some approximate numerical approaches to it have yielded instead a valence bond crystal. We have used the density matrix renormalization group to perform very accurate simulations on numerous cylinders with circumferences up to 12 lattice spacings, finding instead of the valence bond crystal a singlet-gapped spin liquid with substantially lower energy that appears to have \(Z_2\) topological order. Our results, through a combination of very low energy, short correlation lengths and corresponding small finite size effects, a new rigorous energy bound, and consistent behavior on many cylinders, provide strong evidence that the 2D ground state of this model is a gapped spin liquid.