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 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) 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 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.
Detecting Kitaev interactions in real materials remains challenge, as conventional experimental techniques often have difficulty distinguishing fractionalized excitations from other normal contributions. Terahertz two-dimensional coherent spectroscopy (2DCS) offers a novel approach for probing many-body phenomena, such as exotic excitations in quantum magnets. Motivated by recent experiments on CoNb2O6 and the development of the terahertz spectroscopy in Kitaev quantum spin liquid, we proposed a twisted Kitaev model for CoNb2O6 and determined the precise twist angle according to experimental specific-heat phase diagram. With this calibrated model, we found that non-rephasing diagonal and rephasing anti-diagonal signals appear in the 2DCS nonlinear response. The x and y components of the spin superexchange interactions split the rephasing signals into a grid of discrete peaks. We further demonstrate that the diagonal and the discrete rephasing signals primarily originate from two-spinon and four-spinon excitation processes based on numerical projection method. These findings indicate that even weak Kitaev interactions in quantum materials can be effectively detected via two-dimensional coherent spectroscopy .
Abstract With recent advances in terahertz (THz) sources and detection, two-dimensional coherent spectroscopy (2DCS), which allows one to probe nonlinear responses, now reaches the meV regime relevant for quasiparticle excitations in magnetic materials. This opens a promising route to reveal many-body phenomena that evade linear-response probes. To date, most experimental applications have focused on classical magnets, and a solid demonstration in a quantum magnet has yet to be established. Here we present a theoretical study of 2DCS in CoNb 2 O 6 , a quasi-one-dimensional Ising magnet that is believed to host fractionalized spinons which at low temperatures are confined by weak interchain coupling. Our analysis, which builds on an experimentally constrained effective S = 1/2 Hamiltonian, is found to reveal unambiguous 2DCS signatures of spinon deconfinement above the low-temperature ordered phase. Using a four-spinon approximation, we track these 2DCS signatures by sequentially building a faithful microscopic model for CoNb 2 O 6 , starting from the exactly solvable one-dimensional transverse-field Ising model (1 d TFIM) and successively adding additional interactions. In particular, adding a bond-dependent staggered YZ interaction to the 1 d -TFIM already reproduces many key spectral features of the full material Hamiltonian. Within this TFIM+YZ model, we find a series of bound states, including a four-spinon bound state that is distinct from the familiar two-spinon bound states. We further find that introducing a confinement potential suppresses sharp spinon-echo features, which are thought to reflect an underlying continuum of fractionalized excitations. Our results provide concrete predictions for future THz 2DCS experiments on CoNb 2 O 6 and related quasi-one-dimensional quantum magnets.
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.
We investigate the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using the theory of two-dimensional (2D) coherent spectroscopy. We observe that at the isotropic point in the non-Abelian phase of this model, the nonlinear spectrum in the 2D frequency domain consists of sharp signals that originate from the flux excitations and Majorana bound states. Signatures of different flux excitations can be clearly observed in this spectrum, such that one can observe evidences of flux states with 4-adjacent, 2-nonadjacent, and 4-far-separated fluxes, which are not visible in linear response spectroscopy such as neutron scattering experiments. Moreover, in the Abelian phase we perceive that the spectrum in the frequency domain is composed of streak signals. These signals, as in the nonlinear response of the pure Kitaev model, represent a distinct signature of itinerant Majorana fermions. However, deep in the Abelian phase whenever a Kitaev exchange coupling is much stronger than the others, the streak signals are weakened and only single sharp spots are seen in the response, which resembles the dispersionless response of the conventional toric code.