Measuring spin-charge separation by an off-diagonal dissipative response

Abstract Spin-charge separation in the 1D Hubbard model is a paradigmatic example of quantum fractionalization described by decoupled charge and spin sectors of a Tomonaga-Luttinger liquid. Despite the success in measuring velocity differences, it remains challenging to probe emergent excitations' anomalous dimensions experimentally. We propose an off-diagonal dissipative response protocol, leveraging dissipative response theory (DRT), to directly detect spin-charge separation. By selectively dissipating spin-$\downarrow$ particles and measuring the spin-$\uparrow$ response, we uncover a universal temporal crossover: the response grows as $t^3$ at short times and crosses over to linear-in-$t$ growth at long times. Specifically, the intersection time \(t^*(\ell)\) between the short-time \(t^3\) and long-time linear growth exhibits a linear dependence on \(\ell\), whose slope is proportional to \(1/\Delta u\) with a prefactor that depends on the filling \(n\), with negligible residual dependence on \(U\) over a broad parameter range. This prefactor cancels when comparing slopes at a fixed \(n\), allowing the relative variation of \(\Delta u\) with interaction strength to be extracted directly without any absolute calibration. Concurrently, the coefficient of the short-time $t^3$ law encodes the sum of anomalous dimensions $\eta_c+\eta_s$ through its spatial power-law decay. This response signal vanishes in the noninteracting limit, where spin and charge are not separated. Our predictions, verified numerically via tDMRG with microscopic parameters linked to Luttinger parameters by Bethe-ansatz, establish off-diagonal dissipative response as a self-contained probe of quantum fractionalization in synthetic quantum matter.