Nonlinear light cone spreading of correlations in a triangular quantum magnet: a hard quantum simulation target

TL;DR

This study measures real-space, time-resolved spin correlations in the 2D triangular magnet KYbSe$_2$ by extracting the Van Hove function $G(r,t)$ from inelastic neutron scattering and benchmarks it against multiple theories of the triangular Heisenberg model. The key finding is a nonlinear, sub-ballistic light cone with dynamical exponent $z\approx1.4$ that none of the state-of-the-art methods reproduce, signaling emergent hydrodynamic behavior near a proximate quantum spin liquid and establishing KYbSe$_2$ as a demanding quantum-simulation benchmark. The work demonstrates the diagnostic power of real-space correlators and highlights the need for new quantum simulation and HPC approaches to capture collective dynamics beyond quasiparticle pictures. Together, these results map a path toward validating quantum simulators and deepen our understanding of spin-liquid–like critical dynamics in frustrated magnets.

Abstract

Dynamical correlations of quantum many-body systems are typically analyzed in the momentum space and frequency basis. However, quantum simulators operate more naturally in real space, real time settings. Here we analyze the real-space time-dependent van Hove spin correlations $G(r,t)$ of the 2D triangular antiferromagnet KYbSe$_2$ as obtained from high-resolution Fourier-transformed neutron spectroscopy. We compare this to $G(r,t)$ from five theoretical simulations of the well-established spin Hamiltonian. Our analysis reveals non-linear sub-ballistic low-temperature transport in KYbSe$_2$ which none of the current state-of-the-art numerical or field-theoretical methods reproduce. Our observation signals an emergent collective hydrodynamics, perhaps associated with the quantum critical phase of a quantum spin liquid, and provides an ideal benchmark for future quantum simulations.

Figures (19)

• Figure 1: Schematic of generating triangular-lattice real-space correlations. $S(q,\omega)$, which gives spin correlations in reciprocal space and frequency, is Fourier transformed into $G(r,t)$, which gives spin correlations in real-space and time.
• Figure 2: Van Hove correlations for KYbSe$_2$ (a)-(f) and various theoretical models: linear spin wave theory (LSWT) (g)-(l), Schwinger bosons (m)-(r), finite-temperature Landau-Lifshitz dynamics (LL) (s)-(x), $U(1)$ random phase approximation (RPA) simulations (y)-(dd), and matrix product state (MPS) calculations on a six-site circumference cylinder (ee)-(jj). The left column shows the spectra along high-symmetry directions, the second column shows the $t=0$ spin correlation pattern (red indicates ferromagnetic spin correlation, blue indicates antiferromagnetic spin correlation). The third and fourth columns show the real and imaginary spin correlations along the first neighbor crystallographic direction $b$ [vertical blue line in panel (b)]. Columns five and six show the real and imaginary spin correlations along the second neighbor crystallographic direction ${\bf a+b}/2$ [horizontal green line in panel (b)]. Light cones are clearly visible in all cases, but poor agreement is found with LSWT whereas much better agreement is found with the Schwinger Boson and LL calculations.
• Figure 3: Sub-ballistic transport in KYbSe$_2$. Panels (a)-(d) and (f)-(i) show the light cones of KYbSe$_2$ alongside various theoretical models, where the black points show the onset (defined as the midpoint of the rist in $G(r,t)$). Panels (e) and (j) plot the onset time versus distance. The solid lines are fitted to $t_{\rm onset} = A(r^z)$ where $A$ and $z$ are fitted constants (both directions fitted simultaneously). The fitted exponents are listed in panel (j), with the experimental KYbSe$_2$ noticeably deviating from the theoretical simulations. Instead of being in a ballistic regime ($z \approx 1$), the KYbSe$_2$ light cone exhibits sub-ballistic superdiffusive behavior ($z \approx 1.5$).
• Figure S.1: Constant time slices of $G(r,t)$ in KYbSe$_2$. Panels (a)-(l) show the data at 0.3 K, panels (m)-(x) show the data at 1 K, and panels (y)-(jj) show the data at 2 K. The top row in each temperature shows the real part of $G(r,t)$, and the bottom row shows the imaginary part.
• Figure S.2: Quantum Fisher Information Matrix (QFIM) of KYbSe$_2$. Panels (a)-(c) show colormaps of the QFIM at the measured temperatures. Note that the third neighbor correlations nearly vanish at 0.3 K and entirely vanish at 1 K. Panel (d) shows the absolute value of the correlations as a function of distance, and an exponential fit to extract a quantum correlation length (which excludes the sites where correlations are much smaller than neighbors). Closed symbols indicate fitted points, open symbols indicate excluded points. Error bars indicate one standard deviation uncertainty.