Measuring Spin-Charge Separation by an Off-diagonal Dissipative Response

Abstract

Fractionalization of symmetry - exemplified by spin-charge separation in the 1D Hubbard model and fractional charges in the fractional quantum Hall effect - is a typical strongly correlated phenomena in quantum many-body systems. Despite the success in measuring velocity differences, however, it is still quite challenging in probing emergent excitations' anomalous dimensions experimentally. We propose a 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 signature: the off-diagonal response exhibits a crossover from cubic-in-time ($t^3$) growth at short times to linear-in-time ($t$) decay at long times. Crucially, the coefficients $\varkappa^s$ (short-time) and $\varkappa^l$ (long-time) encode the distinct anomalous dimensions and velocities of spinons and holons, providing unambiguous evidence of fractionalization. This signal vanishes trivially without spin-charge separation. Our predictions, verified numerically via tDMRG, with microscopic parameters linking with Luttinger parameters by Bethe ansatz, establish off-diagonal dissipative response as a probe of quantum fractionalization in synthetic quantum matter.

Figures (2)

• Figure 1: (a) Real part of $\delta{\cal W}(\ell,t)$ versus time for $\ell = 1$ under three different densities $n$, comparing PBC with $L = 30$ (colored shapes) and OBC with $L = 50$ (lines). (b) Finite-size scaling analysis for the convergency of PBC and OBC results is performed at three time points along the evolution curve in (a) for $n = 1.0$. (c-d) Real part of $\delta{\cal W}(\ell,t)$ versus time at $\ell = 0.5$ on a log-log scale for $n = 0.6$ and 0.8, respectively, in a system of size $L=50$. Black dashed and dotted lines indicate reference slopes for $t^3$ and $t$, respectively. In all calculations, the interaction is fixed at $U = 5$.
• Figure 2: (a,b) The short-time coefficient $\varkappa^{s}(\ell)$ obtained from tDMRG simulations (colored dots) for $U = 3,5,7$, compared with the analytical approximation (solid lines, Eq. (\ref{['STI']})) and the exact numerical integration of Od-DRT (black dashed lines, Eq. (\ref{['Od_DRT_B']})). (c,d) Corresponding results after removing oscillations, revealing the power-law dependence in $\varkappa^s(\ell)$. Panels (c) and (d) are derived from the data in (a) and (b), respectively. (e) Extracted $\eta_{c} + \eta_{s}$ as a function of $U$, compared with Bethe ansatz results PRL-64-2831Hubbardbook. (f) The optimal overall amplitude as a function of $U$. One can see the curve is better fitted in $n=0.8$ then $n=0.6$.