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arXiv:2205.12822 · Physical review. B./Physical review. B

Spin dynamics and continuum spectra of the honeycomb J 1 − J 2 antiferromagnetic Heisenberg model

Cheng Gu, Shun-Li Yu, Jian‐Xin Li

Published May 9, 2022• 10 citations
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Abstract

We employ the spin cluster perturbation theory to investigate the dynamical properties of the antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the honeycomb lattice. We obtain the excitation spectra for all possible phases in the phase diagram, including the N\'eel phase, plaquette valence-bond-solid phase, dimer valence-bond-solid phase, and stripe antiferromagnetic phase. In the N\'eel phase, besides the obvious renormalization of the magnon dispersion, we find that the spectrum exhibits a dome-shaped broad continuum around the second Brillouin zone (BZ) and the additional strong continuum close to the corner of the BZ. In the valence-bond-solid phases, the spectra are dominated by a strong broad continuum all the way down to below ${J}_{1}$ coexisting with the lowest-energy triplon modes characterizing the plaquette and dimer phases. We ascribe this strong broad continuum and the additional continuum close to the BZ corner in the N\'eel phase to the contributions of fractionalized spinon excitations. In the stripe phase, a clear difference from the linear-spin-wave approximation is that the spectrum is gapped at the $M$ point, while that obtained by the latter is gapless due to the strong quantum fluctuations. We point out that the features observed in the N\'eel phase are consistent with the recent neutron scattering experiments on ${\mathrm{YbCl}}_{3}$ and ${\mathrm{YbBr}}_{3}$.

DOI
10.1103/physrevb.105.174403

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Strongly correlated systems with geometric frustrations can host the emergent phases of matter with unconventional properties. Here, we study the spin S=1S=1S=1 Heisenberg model on the honeycomb lattice with the antiferromagnetic first- (J1{J}_{1}J1​) and second-neighbor (J2{J}_{2}J2​) interactions ($0.0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$) by means of density-matrix renormalization group. In the parameter regime ${J}_{2}/{J}_{1}\ensuremath{\lesssim}0.27$, the system sustains a N\'eel antiferromagnetic phase. At the large J2{J}_{2}J2​ side ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.32$, a stripe antiferromagnetic phase is found. Between the two magnetic ordered phases $0.27\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.32$, we find a nonmagnetic intermediate region with a plaquette valence-bond order. Although our calculations are limited within a six unit-cell width on cylinder, we present evidence that this plaquette state could be a strong candidate for this nonmagnetic region in the thermodynamic limit. We also briefly discuss the nature of the quantum phase transitions in the system. We gain further insight into the nonmagnetic phases in the spin-1 system by comparing its phase diagram with the spin-1/21/21/2 system.
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