Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2502.01746 · Physical Review Research

Nonlinear spectroscopy as a magnon breakdown diagnosis and its efficient simulation

David A. S. Kaib, Marius Möller, Roser Valentí

Published Dec 23, 2025• 3 citations
arXivHTMLPDF

Abstract

Identifying quantum spin liquids, magnon breakdown, or fractionalized excitations in quantum magnets is an ongoing challenge due to the ambiguity in interpreting excitation continua occurring in linear-response probes. Recently, it was proposed that techniques measuring higher-order response, such as two-dimensional coherent spectroscopy (2DCS), could resolve such ambiguities. Numerically simulating nonlinear response functions can, however, be computationally very demanding. We present an efficient Lanczos-based method to compute second-order susceptibilities χ 2 ( ω t , ω τ ) directly in the frequency domain. Applying this to extended Kitaev models describing α − RuCl 3 , we find qualitatively different nonlinear responses between intermediate magnetic field strengths and the high-field regime. To put these results into context, we derive the general 2DCS response of partially polarized magnets within the linear spin-wave approximation, establishing that χ 2 ( ω t , ω τ ) is restricted to a distinct universal form if the excitations are conventional magnons. Deviations from this form, as predicted in our Lanczos-based simulations for α − RuCl 3 , can hence serve in 2DCS experiments as direct criteria to determine whether an observed excitation continuum is of conventional two-magnon type or of different nature.

DOI
10.1103/h5sd-flyf

Related papers

Disentangling spin excitation continua in classical and quantum magnets using 2D nonlinear spectroscopy

Emily Z. Zhang, Ciarán Hickey, Yong Baek Kim

Inelastic neutron scattering (INS) has traditionally been one of the primary methods for investigating quantum magnets, particularly in identifying a continuum of excitations as a hallmark of spin fractionalization in quantum spin liquids (QSLs). However, INS faces severe limitations due to its inability to distinguish between such QSL signatures and similar excitation continua arising from highly frustrated magnetic orders with large unit cells or classical spin liquids. In contrast, two-dimensional coherent spectroscopy (2DCS) has emerged as a powerful tool to probe nonlinear excitation dynamics, offering insights into the underlying mechanisms behind these broad spectral features. In this paper, we utilize classical molecular dynamics (MD) techniques to explore the 2DCS responses of frustrated magnets with dominant Kitaev interactions. Comparing the classical and quantum versions of the pure Kitaev model our results indicate both clear similarities, in the form of sharp line features, and clear distinctions, in the locations of these features and in selection rules. Moreover, in the extended $KΓΓ'$ model, we show that the 2DCS response of the Kitaev spin liquid is completely distinct from that of large unit cell magnetic orders, despite both generating a broad continuum in INS. Additionally, we demonstrate the extreme sensitivity of classical 2DCS to thermal fluctuations and discuss the potential significance of quantum coherence in experimental settings. Overall, our work illustrates the potential of 2DCS in resolving the complex physics underlying ambiguous spin excitation continua, thereby enhancing our understanding of the dynamics in these frustrated systems.

arXiv:2404.16935•Apr 25, 2024•0 citations

Probing Majorana Wave Functions in Kitaev Honeycomb Spin Liquids with Second-Order Two-Dimensional Spectroscopy

Yihua Qiang, Victor L. Quito, Thaís V. Trevisan +1 more

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ_{yzx}^{(2)}(ω_{1},ω_{2}) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z_{2} flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wave functions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our Letter can guide future 2DCS experiments on Kitaev magnets.

Physical Review Letters•Sep 20, 2024•15 citations

Probing Majorana wavefunctions in Kitaev honeycomb spin liquids with second-order two-dimensional spectroscopy

Yihua Qiang, Victor L. Quito, Thaís V. Trevisan +1 more

Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response $χ^{(2)}_{yzx}(ω_1, ω_2)$ when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by $\mathbb{Z}_2$ flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wavefunctions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our work can guide future 2DCS experiments on Kitaev magnets.

arXiv:2301.11243•Jan 26, 2023•3 citations

Theory of nonlinear spectroscopy of quantum magnets

Anubhav Srivastava, Stefan Birnkammer, GiBaik Sim +2 more

Two-dimensional coherent spectroscopy (2DCS) is an established method for characterizing molecules and has been proposed in the terahertz regime as a tool for probing exotic excitations of quantum magnets; however, the precise nature of the coupling between pump field and spin degrees of freedom has remained unclear. Here, we develop a general response theory of 2DCS and show how magnetoelectric as well as polarization couplings contribute to 2DCS in addition to the typically assumed magnetization. We propose experimental protocols to probe the presence of polarization couplings, for instance, from exchange-striction or spin-current mechanism, when the electric field couples to quadratic terms in spin operators. We provide example calculations for the paradigmatic twisted Kitaev chain material CoNb 2 O 6 and highlight the crucial role of contributions from cross-coupling between polarization and magnetic nonlinear susceptibilities. Our work paves the way for systematic studies of light-matter couplings in quantum magnets and for establishing 2DCS as a versatile tool for probing fractional excitations of exotic magnetic quantum phases.

arXiv:2502.17554•Physical review. B./Physical review. B•Mar 20, 2026•0 citations

Revealing Quadrupolar Excitations with Nonlinear Spectroscopy

Yoshito Watanabe, Simon Trebst, Ciarán Hickey

Local moments with a spin S>1/2 can exhibit a rich variety of elementary quasiparticle excitations, such as quadrupolar excitations, that go beyond the dipolar magnons of conventional spin-1/2 systems. However, the experimental observation of such quadrupolar excitations is often challenging due to the dipolar selection rules of many linear response probes, rendering them invisible. Here we show that nonlinear spectroscopy, in the form of two-dimensional coherent spectroscopy (2DCS), can be used to reveal quadrupolar excitations. Considering a family of spin-1 Heisenberg ferromagnets with single-ion easy-axis anisotropy as an example, we explicitly calculate their 2DCS signature by combining exact diagonalization and generalized spin wave theory. We further demonstrate that 2DCS can provide access to the quadrupolar weight of an excitation, analogous to how linear response provides access to the dipolar weight. Our work highlights the potential of nonlinear spectroscopy as a powerful tool to diagnose multipolar excitations in quantum magnets.

arXiv:2405.14954•Physical Review Letters•Mar 14, 2025•6 citations

Exploiting polarization dependence in two-dimensional coherent spectroscopy: Examples of Ce 2 Zr 2 O 7 and Nd 2 Zr 2 O 7

Mark Potts, Roderich Moessner, Owen Benton

Two-dimensional coherent spectroscopy (2DCS) probes the nonlinear optical response of correlated systems. An interesting application is the study of fractionalized excitations, which are challenging to distinguish unambiguously in linear response. Here we demonstrate how the sensitivity of optical matrix elements to variations in the photon polarization allows one to probe different aspects of low-lying excitations in models of the candidate fractionalized materials Ce 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 , which host effective one-dimensional spin chains when subjected to a [110] magnetic field. We show how both fractionalized spinon excitations or conventional magnons can be picked out in the 2DCS response and how the response from polarized spin chains can be used to probe the dipolar-octupolar mixing angle θ through the relative intensity of one- and two-magnon signals. Further, we find that a [001] polarization of the probe field is particularly sensitive to lower band edge of the spinon continuum and can be used as a measure of the proximity of a quantum critical point in Ce 2 Zr 2 O 7 . 2DCS can thus be employed to provide invaluable and detailed information both on the constituent degrees of freedom of a quantum material and on their collective behavior. Published by the American Physical Society 2024

arXiv:2311.03200•Physical review. B./Physical review. B•Mar 29, 2024•8 citations
Identifying quantum spin liquids, magnon breakdown, or fractionalized excitations in quantum magnets is an ongoing challenge due to the ambiguity in interpreting excitation continua occurring in linear-response probes. Recently, it was proposed that techniques measuring higher-order response, such as two-dimensional coherent spectroscopy (2DCS), could resolve such ambiguities. Numerically simulating nonlinear response functions can, however, be computationally very demanding. We present an efficient Lanczos-based method to compute second-order susceptibilities χ 2 ( ω t , ω τ ) directly in the frequency domain. Applying this to extended Kitaev models describing α − RuCl 3 , we find qualitatively different nonlinear responses between intermediate magnetic field strengths and the high-field regime. To put these results into context, we derive the general 2DCS response of partially polarized magnets within the linear spin-wave approximation, establishing that χ 2 ( ω t , ω τ ) is restricted to a distinct universal form if the excitations are conventional magnons. Deviations from this form, as predicted in our Lanczos-based simulations for α − RuCl 3 , can hence serve in 2DCS experiments as direct criteria to determine whether an observed excitation continuum is of conventional two-magnon type or of different nature.
Inelastic neutron scattering (INS) has traditionally been one of the primary methods for investigating quantum magnets, particularly in identifying a continuum of excitations as a hallmark of spin fractionalization in quantum spin liquids (QSLs). However, INS faces severe limitations due to its inability to distinguish between such QSL signatures and similar excitation continua arising from highly frustrated magnetic orders with large unit cells or classical spin liquids. In contrast, two-dimensional coherent spectroscopy (2DCS) has emerged as a powerful tool to probe nonlinear excitation dynamics, offering insights into the underlying mechanisms behind these broad spectral features. In this paper, we utilize classical molecular dynamics (MD) techniques to explore the 2DCS responses of frustrated magnets with dominant Kitaev interactions. Comparing the classical and quantum versions of the pure Kitaev model our results indicate both clear similarities, in the form of sharp line features, and clear distinctions, in the locations of these features and in selection rules. Moreover, in the extended KΓΓ′KΓΓ'KΓΓ′ model, we show that the 2DCS response of the Kitaev spin liquid is completely distinct from that of large unit cell magnetic orders, despite both generating a broad continuum in INS. Additionally, we demonstrate the extreme sensitivity of classical 2DCS to thermal fluctuations and discuss the potential significance of quantum coherence in experimental settings. Overall, our work illustrates the potential of 2DCS in resolving the complex physics underlying ambiguous spin excitation continua, thereby enhancing our understanding of the dynamics in these frustrated systems.
Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χ_{yzx}^{(2)}(ω_{1},ω_{2}) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z_{2} flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wave functions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our Letter can guide future 2DCS experiments on Kitaev magnets.
Two-dimensional coherent terahertz spectroscopy (2DCS) emerges as a valuable tool to probe the nature, couplings, and lifetimes of excitations in quantum materials. It thus promises to identify unique signatures of spin liquid states in quantum magnets by directly probing properties of their exotic fractionalized excitations. Here, we calculate the second-order 2DCS of the Kitaev honeycomb model and demonstrate that distinct spin liquid fingerprints appear already in this lowest-order nonlinear response χyzx(2)(ω1,ω2)χ^{(2)}_{yzx}(ω_1, ω_2)χyzx(2)​(ω1​,ω2​) when using crossed light polarizations. We further relate the off-diagonal 2DCS peaks to the localized nature of the matter Majorana excitations trapped by Z2\mathbb{Z}_2Z2​ flux excitations and show that 2DCS thus directly probes the inverse participation ratio of Majorana wavefunctions. By providing experimentally observable features of spin liquid states in the 2D spectrum, our work can guide future 2DCS experiments on Kitaev magnets.
Two-dimensional coherent spectroscopy (2DCS) is an established method for characterizing molecules and has been proposed in the terahertz regime as a tool for probing exotic excitations of quantum magnets; however, the precise nature of the coupling between pump field and spin degrees of freedom has remained unclear. Here, we develop a general response theory of 2DCS and show how magnetoelectric as well as polarization couplings contribute to 2DCS in addition to the typically assumed magnetization. We propose experimental protocols to probe the presence of polarization couplings, for instance, from exchange-striction or spin-current mechanism, when the electric field couples to quadratic terms in spin operators. We provide example calculations for the paradigmatic twisted Kitaev chain material CoNb 2 O 6 and highlight the crucial role of contributions from cross-coupling between polarization and magnetic nonlinear susceptibilities. Our work paves the way for systematic studies of light-matter couplings in quantum magnets and for establishing 2DCS as a versatile tool for probing fractional excitations of exotic magnetic quantum phases.
Local moments with a spin S>1/2 can exhibit a rich variety of elementary quasiparticle excitations, such as quadrupolar excitations, that go beyond the dipolar magnons of conventional spin-1/2 systems. However, the experimental observation of such quadrupolar excitations is often challenging due to the dipolar selection rules of many linear response probes, rendering them invisible. Here we show that nonlinear spectroscopy, in the form of two-dimensional coherent spectroscopy (2DCS), can be used to reveal quadrupolar excitations. Considering a family of spin-1 Heisenberg ferromagnets with single-ion easy-axis anisotropy as an example, we explicitly calculate their 2DCS signature by combining exact diagonalization and generalized spin wave theory. We further demonstrate that 2DCS can provide access to the quadrupolar weight of an excitation, analogous to how linear response provides access to the dipolar weight. Our work highlights the potential of nonlinear spectroscopy as a powerful tool to diagnose multipolar excitations in quantum magnets.
Two-dimensional coherent spectroscopy (2DCS) probes the nonlinear optical response of correlated systems. An interesting application is the study of fractionalized excitations, which are challenging to distinguish unambiguously in linear response. Here we demonstrate how the sensitivity of optical matrix elements to variations in the photon polarization allows one to probe different aspects of low-lying excitations in models of the candidate fractionalized materials Ce 2 Zr 2 O 7 and Nd 2 Zr 2 O 7 , which host effective one-dimensional spin chains when subjected to a [110] magnetic field. We show how both fractionalized spinon excitations or conventional magnons can be picked out in the 2DCS response and how the response from polarized spin chains can be used to probe the dipolar-octupolar mixing angle θ through the relative intensity of one- and two-magnon signals. Further, we find that a [001] polarization of the probe field is particularly sensitive to lower band edge of the spinon continuum and can be used as a measure of the proximity of a quantum critical point in Ce 2 Zr 2 O 7 . 2DCS can thus be employed to provide invaluable and detailed information both on the constituent degrees of freedom of a quantum material and on their collective behavior. Published by the American Physical Society 2024