Collective excitations in chiral spin liquid: chiral roton and long-wavelength nematic mode

Hongyu Lu; Wei Zhu; Wang Yao

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arXiv · 2601.20702

Collective excitations in chiral spin liquid: chiral roton and long-wavelength nematic mode

Hongyu Lu·Wei Zhu·Wang Yao

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Abstract

Chiral spin liquid (CSL) is a magnetic analogue of the fractional quantum Hall (FQH) liquid. Collective excitations play a vital role in shaping our understanding of these exotic quantum phases of matter and their quantum phase transitions. While the magneto-roton and long-wavelength chiral graviton modes in the FQH and fractional Chern insulator (FCI) liquids have been extensively explored, whether CSLs host analogous or qualitatively different modes remains elusive. Here we explore the collective excitations in the SU(2) symmetric CSL phase. Combining exact diagonalization and time-dependent variational principle calculations, we identify two spin-singlet collective modes: a chiral p-wave roton mode at finite momentum, and a elliptically polarized d-wave nematic mode at zero momentum, both of which are prominent across the CSL phase. The chiral p-wave singlet roton has no counterpart in FQH of FCI systems, and the q = 0 d-wave mode also exhibits fingerprint distinct from those of FQH/FCI liquids. We also elucidate that both singlet modes are general for CSLs on various lattice models. By tuning J2, we find the nematic mode to be pronouncedly soft, together with the spin-triplet two-spinon bound states, potentially promoting strong nematic and spin stripe instabilities. Our work paves the way for further understanding CSL from the dynamical perspective and provides new spectroscopic signatures for future experiments of CSL candidates.

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Hongyu Lu, Wei Zhu, Wang Yao. 2026-09-18. Collective excitations in chiral spin liquid: chiral roton and long-wavelength nematic mode. https://arxiv.org/abs/2601.20702

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