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Raman circular dichroism and spinon quantum geometry of chiral quantum spin liquids
Phys. Rev. B 114, 194425 – Published 26 October, 2026
DOI: https://doi.org/10.1103/n6zn-xvsw
Abstract
We show that the quantum geometry of fractionalized spin excitations in Mott-insulating quantum spin liquids (QSLs) gives rise to a finite Raman circular dichroism (RCD) signal. We identify conditions under which the Loudon-Fleury framework, where light modulates the underlying exchange interactions, and the light-matter-coupling approach, where the effective vector potential couples directly to the spinon bands, yield equivalent Raman vertices for the fractionalized quasiparticles. Using the latter, we derive an analytical decomposition of the RCD into different quantum geometric contributions. This reveals the sensitivity of the RCD to the underlying structure of the wave functions and the handedness of the excitations, rather than a nonzero Chern number of spinon excitations. To illustrate this, we apply our approach to two examples, the Kitaev honeycomb model in a magnetic field and a parton mean-field state of the chiral QSL on the triangular lattice.
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References (78)
- M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. London A 392, 45 (1984).
- P. Törmä, Essay: Where can quantum geometry lead us? Phys. Rev. Lett. 131, 240001 (2023).
- J. Yu, B. A. Bernevig, R. Queiroz, E. Rossi, P. Törmä, and B.-J. Yang, Quantum geometry in quantum materials, npj Quantum Materials 10, 101 (2025).
- D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
- D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49, 405 (1982).
- Q. Niu, D. J. Thouless, and Y.-S. Wu, Quantized Hall conductance as a topological invariant, Phys. Rev. B 31, 3372 (1985).
- C. L. Kane and E. J. Mele, topological order and the quantum spin Hall effect, Phys. Rev. Lett. 95, 146802 (2005).
- D. N. Sheng, Z. Y. Weng, L. Sheng, and F. D. M. Haldane, Quantum spin-hall effect and topologically invariant chern numbers, Phys. Rev. Lett. 97, 036808 (2006).
- C. M. Canali, A. Cehovin, and A. H. MacDonald, Chern numbers for spin models of transition metal nanomagnets, Phys. Rev. Lett. 91, 046805 (2003).
- K. v. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance, Phys. Rev. Lett. 45, 494 (1980).
- R. B. Laughlin, Quantized hall conductivity in two dimensions, Phys. Rev. B 23, 5632 (1981).
- C. L. Kane and M. P. A. Fisher, Quantized thermal transport in the fractional quantum hall effect, Phys. Rev. B 55, 15832 (1997).
- A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Phys. 321, 2 (2006).
- Y. Kasahara, T. Ohnishi, Y. Mizukami, O. Tanaka, S. Ma, K. Sugii, N. Kurita, H. Tanaka, J. Nasu, Y. Motome, T. Shibauchi, and Y. Matsuda, Majorana quantization and half-integer thermal quantum hall effect in a kitaev spin liquid, Nature (London) 559, 227 (2018).
- A. Raoux, F. Piéchon, J.-N. Fuchs, and G. Montambaux, Orbital magnetism in coupled-bands models, Phys. Rev. B 91, 085120 (2015).
- J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Commun. Math. Phys. 76, 289 (1980).
- E. Study, Körzeste Wege im komplexen Gebiet, Math. Ann. 60, 321 (1905).
- G. Fubini, On a Metric defined by a Hermitian form, Atti Inst. Veneto Sci. Lett. Arti 63, 501 (1904).
- F. Piéchon, A. Raoux, J.-N. Fuchs, and G. Montambaux, Geometric orbital susceptibility: Quantum metric without berry curvature, Phys. Rev. B 94, 134423 (2016).
- Y. Jiang, T. Holder, and B. Yan, Revealing quantum geometry in nonlinear quantum materials, Rep. Prog. Phys. 88, 076502 (2025).
- N. Marzari and D. Vanderbilt, Maximally localized generalized wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997).
- C. Brouder, G. Panati, M. Calandra, C. Mourougane, and N. Marzari, Exponential localization of wannier functions in insulators, Phys. Rev. Lett. 98, 046402 (2007).
- N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012).
- Y. Gao, S. A. Yang, and Q. Niu, Field induced positional shift of bloch electrons and its dynamical implications, Phys. Rev. Lett. 112, 166601 (2014).
- T. Morimoto and N. Nagaosa, Topological nature of nonlinear optical effects in solids, Sci. Adv. 2, e1501524 (2016).
- J. Ahn, G.-Y. Guo, N. Nagaosa, and A. Vishwanath, Riemannian geometry of resonant optical responses, Nat. Phys. 18, 290 (2022).
- S. Peotta and P. Törmä, Superfluidity in topologically nontrivial flat bands, Nat. Commun. 6, 8944 (2015).
- A. Julku, S. Peotta, T. I. Vanhala, D.-H. Kim, and P. Törmä, Geometric origin of superfluidity in the lieb-lattice flat band, Phys. Rev. Lett. 117, 045303 (2016).
- L. Liang, T. I. Vanhala, S. Peotta, T. Siro, A. Harju, and P. Törmä, Band geometry, berry curvature, and superfluid weight, Phys. Rev. B 95, 024515 (2017).
- P. Törmä, L. Liang, and S. Peotta, Quantum metric and effective mass of a two-body bound state in a flat band, Phys. Rev. B 98, 220511(R) (2018).
- J. Herzog-Arbeitman, A. Chew, K.-E. Huhtinen, P. Törmä, and B. A. Bernevig, Many-body superconductivity in topological flat bands, Commun. Phys. (2026), https://doi.org/10.1038/s42005-026-02732-2.
- P. Törmä, S. Peotta, and B. A. Bernevig, Superconductivity, superfluidity and quantum geometry in twisted multilayer systems, Nat. Rev. Phys. 4, 528 (2022).
- S. Peotta, K.-E. Huhtinen, and P. Törmä, Quantum geometry in superfluidity and superconductivity, Proc. Intl. School Phys. Enrico Fermi 211, 373 (2025).
- G. Salerno, T. Ozawa, and P. Törmä, Drude weight and the many-body quantum metric in one-dimensional bose systems, Phys. Rev. B 108, L140503 (2023).
- X.-C. Wu, K.-L. Cai, M. Cheng, and P. Kumar, Corner charge fluctuations and many-body quantum geometry, Phys. Rev. B 111, 115124 (2025).
- E. Fradkin, Field Theories of Condensed Matter Physics (Cambridge University Press, Cambridge, 2013).
- P. A. McClarty, Topological magnons: A review, Annu. Rev. Condens. Matter Phys. 13, 171 (2022).
- E. Viñas Boström, T. S. Parvini, J. W. McIver, A. Rubio, S. V. Kusminskiy, and M. A. Sentef, Direct optical probe of magnon topology in two-dimensional quantum magnets, Phys. Rev. Lett. 130, 026701 (2023).
- L. Savary and L. Balents, Quantum spin liquids: a review, Rep. Prog. Phys. 80, 016502 (2017).
- J. Knolle and R. Moessner, A field guide to spin liquids, Annu. Rev. Condens. Matter Phys. 10, 451 (2019).
- X.-G. Wen, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford University Press, Oxford, UK, 2004).
- V. Kalmeyer and R. B. Laughlin, Equivalence of the resonating-valence-bond and fractional quantum hall states, Phys. Rev. Lett. 59, 2095 (1987).
- J. Knolle, G.-W. Chern, D. L. Kovrizhin, R. Moessner, and N. B. Perkins, Raman scattering signatures of kitaev spin liquids in iridates with or Li, Phys. Rev. Lett. 113, 187201 (2014).
- B. Perreault, J. Knolle, N. B. Perkins, and F. J. Burnell, Theory of raman response in three-dimensional kitaev spin liquids: Application to - and compounds, Phys. Rev. B 92, 094439 (2015).
- J. Nasu, J. Knolle, D. Kovrizhin, Y. Motome, and R. Moessner, Fermionic response from fractionalization in an insulating two-dimensionalmagnet, Nat. Phys. 12, 912 (2016).
- I. Rousochatzakis, S. Kourtis, J. Knolle, R. Moessner, and N. B. Perkins, Quantum spin liquid at finite temperature: Proximate dynamics and persistent typicality, Phys. Rev. B 100, 045117 (2019).
- L. J. Sandilands, Y. Tian, K. W. Plumb, Y.-J. Kim, and K. S. Burch, Scattering continuum and possible fractionalized excitations in , Phys. Rev. Lett. 114, 147201 (2015).
- A. Glamazda, P. Lemmens, S. H. Do, Y. S. Choi, and K. Y. Choi, Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates - and , Nat. Commun. 7, 12286 (2016).
- A. Sahasrabudhe, D. A. S. Kaib, S. Reschke, R. German, T. C. Koethe, J. Buhot, D. Kamenskyi, C. Hickey, P. Becker, V. Tsurkan, A. Loidl, S. H. Do, K. Y. Choi, M. Grüninger, S. M. Winter, Z. Wang, R. Valentí, and P. H. M. van Loosdrecht, High-field quantum disordered state in : Spin flips, bound states, and multiparticle continuum, Phys. Rev. B 101, 140410(R) (2020).
- D. Wulferding, Y. Choi, S.-H. Do, C. H. Lee, P. Lemmens, C. Faugeras, Y. Gallais, and K.-Y. Choi, Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnet , Nat. Commun. 11, 1603 (2020).
- W.-H. Ko, Z.-X. Liu, T.-K. Ng, and P. A. Lee, Raman signature of the U(1) Dirac spin-liquid state in the spin- kagome system, Phys. Rev. B 81, 024414 (2010).
- J. Knolle, Dynamics of a Quantum Spin Liquid (Springer, Cham, 2016).
- P. A. Fleury and R. Loudon, Scattering of light by one- and two-magnon excitations, Phys. Rev. 166, 514 (1968).
- G. E. Topp, C. J. Eckhardt, D. M. Kennes, M. A. Sentef, and P. Törmä, Light-matter coupling and quantum geometry in moiré materials, Phys. Rev. B 104, 064306 (2021).
- R. Kaneko, S. Morita, and M. Imada, Gapless spin-liquid phase in an extended spin 1/2 triangular heisenberg model, J. Phys. Soc. Jpn. 83, 093707 (2014).
- Y. Iqbal, W.-J. Hu, R. Thomale, D. Poilblanc, and F. Becca, Spin liquid nature in the heisenberg triangular antiferromagnet, Phys. Rev. B 93, 144411 (2016).
- S.-S. Gong, W. Zheng, M. Lee, Y.-M. Lu, and D. N. Sheng, Chiral spin liquid with spinon fermi surfaces in the spin- triangular heisenberg model, Phys. Rev. B 100, 241111(R) (2019).
- B. S. Shastry and B. I. Shraiman, Theory of raman scattering in mott-hubbard systems, Phys. Rev. Lett. 65, 1068 (1990).
- B. S. Shastry and B. I. Shraiman, Raman scattering in mott-hubbard systems, Intl. J. Mod. Phys. B 05, 365 (1991).
- T. P. Devereaux and R. Hackl, Inelastic light scattering from correlated electrons, Rev. Mod. Phys. 79, 175 (2007).
- J. Fu, J. G. Rau, Michel J. P. Gingras, and N. B. Perkins, Fingerprints of quantum spin ice in raman scattering, Phys. Rev. B 96, 035136 (2017).
- Y. Yang, M. Li, I. Rousochatzakis, and N. B. Perkins, Non-loudon-fleury raman scattering in spin-orbit coupled mott insulators, Phys. Rev. B 104, 144412 (2021).
- M. Onoda, A. S. Mishchenko, and N. Nagaosa, Left-handed spin wave excitation in ferromagnet, J. Phys. Soc. Jpn. 77, 013702 (2008).
- K. Jenni, S. Kunkemöller, W. Schmidt, P. Steffens, A. A. Nugroho, and M. Braden, Chirality of magnetic excitations in ferromagnetic , Phys. Rev. B 105, L180408 (2022).
- K. R. Hoffman, D. J. Lockwood, and W. M. Yen, Circular dichroism and raman optical activity in antiferromagnetic transition-metal fluorides, Low Temp. Phys. 31, 786 (2005).
- S.-F. Liou, F. D. M. Haldane, K. Yang, and E. H. Rezayi, Chiral gravitons in fractional quantum hall liquids, Phys. Rev. Lett. 123, 146801 (2019).
- D. X. Nguyen and D. T. Son, Probing the spin structure of the fractional quantum hall magnetoroton with polarized raman scattering, Phys. Rev. Res. 3, 023040 (2021).
- J. Liang, Z. Liu, Z. Yang, Y. Huang, U. Wurstbauer, C. R. Dean, K. W. West, L. N. Pfeiffer, L. Du, and A. Pinczuk, Evidence for chiral graviton modes in fractional quantum Hall liquids, Nature (London) 628, 78 (2024).
- J. Mitscherling, A. Avdoshkin, and J. E. Moore, Gauge-invariant projector calculus for quantum state geometry and applications to observables in crystals, Phys. Rev. B 112, 085104 (2025).
- E. Lieb, T. Schultz, and D. Mattis, Two soluble models of an antiferromagnetic chain, Ann. Phys. 16, 407 (1961).
- W.-J. Hu, S.-S. Gong, W. Zhu, and D. N. Sheng, Competing spin-liquid states in the spin- heisenberg model on the triangular lattice, Phys. Rev. B 92, 140403(R) (2015).
- S.-S. Gong, W. Zhu, J.-X. Zhu, D. N. Sheng, and K. Yang, Global phase diagram and quantum spin liquids in a spin- triangular antiferromagnet, Phys. Rev. B 96, 075116 (2017).
- A. Wietek and A. M. Läuchli, Chiral spin liquid and quantum criticality in extended heisenberg models on the triangular lattice, Phys. Rev. B 95, 035141 (2017).
- Z. Zhu, P. A. Maksimov, S. R. White, and A. L. Chernyshev, Topography of spin liquids on a triangular lattice, Phys. Rev. Lett. 120, 207203 (2018).
- X.-Y. Song, A. Vishwanath, and Y.-H. Zhang, Doping the chiral spin liquid: Topological superconductor or chiral metal, Phys. Rev. B 103, 165138 (2021).
- A. Sahasrabudhe, M. A. Prosnikov, T. C. Koethe, P. Stein, V. Tsurkan, A. Loidl, M. Grüninger, H. Hedayat, and P. H. M. van Loosdrecht, Chiral excitations and the intermediate-field regime in the kitaev magnet - , Phys. Rev. Res. 6, L022005 (2024).
- E. Koller et al., Raman circular dichroism and spinon quantum geometry of chiral quantum spin liquids, Zenodo, 2025, https://doi.org/10.5281/zenodo.14946046.
- Y. S. Liu, E. V. Boström, M. A. Sentef, and S. V. Kusminskiy, Light-matter-coupling formalism for magnons: probing quantum geometry with light, arXiv:2604.11931.