Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the Kagome lattice

W. Zhu; Shou-shu Gong; D. N. Sheng

doi:10.1073/pnas.1807840116

New Research In

Edited by Cristian D. Batista, University of Tennessee at Knoxville, Knoxville, TN, and accepted by Editorial Board Member Zachary Fisk February 4, 2019 (received for review May 10, 2018)

Significance

In frustrated quantum magnets, the interplay between quantum fluctuation and geometric frustration may prevent magnetic ordering and result in exotic quantum spin liquids, where the spin degrees of freedom form disordered liquid-like states with novel fractionalized excitations. Here, we study the dynamical response of spin liquids on a Kagome lattice Heisenberg antiferromagnet. Our results reproduce the main observations in the inelastic neutron scattering measurements of herbertsmithite and unveil the spin liquid nature of the ground state with fractionalized spinon excitations. By crossing the quantum-phase transition between the spin liquid and magnetically ordered phase, we identify the condensation of two-spinon bound state as the driving force.

Abstract

A spin-1/2 lattice Heisenberg Kagome antiferromagnet (KAFM) is a prototypical frustrated quantum magnet, which exhibits exotic quantum spin liquids that evade long-range magnetic order due to the interplay between quantum fluctuation and geometric frustration. So far, the main focus has remained on the ground-state properties; however, the theoretical consensus regarding the magnetic excitations is limited. Here, we study the dynamic spin structure factor (DSSF) of the KAFM by means of the density matrix renormalization group. By comparison with the well-defined magnetically ordered state and the chiral spin liquid sitting nearby in the phase diagram, the KAFM with nearest neighbor interactions shows distinct dynamical responses. The DSSF displays important spectral intensity predominantly in the low-frequency region around the Q=M point in momentum space and shows a broad spectral distribution in the high-frequency region for momenta along the boundary of the extended Brillouin zone. The excitation continuum identified from momentum- and energy-resolved DSSF signals emergent spinons carrying fractional quantum numbers. These results capture the main observations in the inelastic neutron scattering measurements of herbertsmithite and indicate the spin liquid nature of the ground state. By tracking the DSSF across quantum-phase transition between the chiral spin liquid and the magnetically ordered phase, we identify the condensation of two-spinon bound state driving the quantum-phase transition.

Footnotes

↵¹To whom correspondence may be addressed. Email: phwzhu{at}gmail.com or donna.sheng1{at}csun.edu.

Author contributions: W.Z. designed research; W.Z. and D.N.S. performed research; W.Z., S.-s.G., and D.N.S. analyzed data; and W.Z. and D.N.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission. C.D.B. is a guest editor invited by the Editorial Board.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1807840116/-/DCSupplemental.

Published under the PNAS license.

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