Unveiling the Phase Diagram and Nonlinear Optical Responses of a Twisted Kitaev Chain

TL;DR

This work addresses the challenge of identifying Kitaev interactions in real materials by introducing a twist-aware Kitaev chain model for CoNb2O6 and calibrating the twist angle $\theta$ from the specific-heat phase diagram. It leverages terahertz 2DCS and a Lanczos-based numerical framework to compute the third-order susceptibility $\chi^{(3)}_{\alpha\alpha\alpha\alpha}$, revealing that a finite twist yields diagonal non-rephasing signals and discrete rephasing peaks tied to two-spinon and four-spinon excitations. The results show that even weak Kitaev components can be detected via 2DCS, and that the twist angle serves as a tuning knob for spectral weight and gap, with the $\theta=45^ ext{$\circ$}$ limit approaching a Kitaev-dominated regime. Together with the phase diagram and spinon dynamics, these findings establish 2DCS as a practical tool for probing Kitaev physics in quantum magnets.

Abstract

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 CoNb$_2$O$_6$ and the development of the terahertz spectroscopy in Kitaev quantum spin liquid, we proposed a twisted Kitaev model for CoNb$_2$O$_6$ 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 .

Figures (11)

• Figure 1: (Color online) (a) The twisted Kitaev chain of Co$^{2+}$ ions and distorted O$^{2-}$ octahedraMorris-NatPhys-17-832-2021. The crystalgraphic a,b, and c directions are indicated. (b) $\hat{n}_{1}$ and $\hat{n}_{2}$ are the two alternating Ising direcitons. The $\hat{y}$ spin direction is identified with the b axis. $\theta$ is the twist angle that $\hat{n}_{1}$ and $\hat{n}_{2}$ made with the $\hat{z}$ axis. (c) The laboratory reference frame $[x,y,z]$ and the local reference frame $[x^{\prime},y^{\prime},z^{\prime}]$ with z axis along the spin orientation.
• Figure 2: (Color online) (a) The specific heat of the TKM for different chain length at $\theta$=20°. Insite is the finite-size scaling result. (b) The phase diagrams of the tiwsted Kitaev model inferred from $C/T$ with $\theta$=20° and chain length $L=18$. The solid lines with circle and square symbols are the transition temperature $T_{c}$ and gap $\Delta$Liang-NatCommun-6-7611-2015. The dash lines with hollow circle and square symbols are the finite-size extrapolated numerical results for comparison.
• Figure 3: (Color online) $S^{xx}(k,w)$ obtained by the exact diagonalization on a 20-site cluster with periodic boundary conditions at transverse fields $h=0$
• Figure 4: (Color online) Two-dimensional amplitude spectrum of the third-order susceptibilities $\chi^{(3)}_{xxxx}(\omega_{2},0,\omega_{1})$for $\theta$=0° (a) and $\theta$=20° (b), respectively with chain length $L=18$. .
• Figure 5: (Color online) Two-dimensional amplitude spectrum of the four point correlation functions with $\theta$=20° and chain length $L=18$, (a) Am$\mathcal{F}[\text{Im}R_{xxxx}^{(1)}(\tau_{2},0,\tau_{1})]$ (b) Am$\mathcal{F}[\text{Im}R_{xxxx}^{(2)}(\tau_{2},0,\tau_{1})]$ (c) Am$\mathcal{F}[\text{Im}R_{xxxx}^{(3)}(\tau_{2},0,\tau_{1})]$ (d) Am$\mathcal{F}[\text{Im}R_{xxxx}^{(4)}(\tau_{2},0,\tau_{1})]$. Here $\mathcal{F}$ is the Fourier transformation.