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

TL;DR

This paper proposes a novel off-diagonal dissipative response method to directly detect spin-charge separation in quantum many-body systems, using dissipative response theory and numerical verification to identify fractionalization signatures.

Contribution

It introduces a new protocol leveraging off-diagonal dissipative response to experimentally detect spin-charge separation and fractionalization in quantum systems.

Findings

Universal temporal signature of response crossover from cubic to linear growth.

Coefficients encode anomalous dimensions and velocities of fractionalized excitations.

Numerical verification via tDMRG confirms theoretical predictions.

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.