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Quantum spin liquids (QSLs) are highly entangled ground states of insulatingspin systems, in which magnetic ordering is prevented down to the lowesttemperatures due to quantum fluctuations. One of the most extraordinarycharacteristics of QSL phases is their ability to support fractionalized,low-energy quasiparticles known as spinons, which carry spin-1/2 but bear nocharge. Relaxometry based on color centers in crystalline materials -- of whichnitrogen-vacancy (NV) centers in diamond are a well-explored example --provides an exciting new platform to probe the spin spectral functions ofmagnetic materials with both energy and momentum resolution and to search forsignatures of these elusive, fractionalized excitations. In this work, wetheoretically investigate the color-center relaxometry of two archetypal QSLs:the two-dimensional U(1) QSL with a spinon Fermi surface and the spin-1/2antiferromagnetic spin chain. The former is characterized by a metallic,spin-split ground state of mobile, interacting spinons, which closely resemblesa spin-polarized Fermi liquid ground state but with neutral quasiparticles. Weshow that the observation of the Stoner continuum and the collective spin wavemode in the spin spectral function would provide a strong evidence for theexistence of spinons and fractionalization. In one dimension, mobile spinonsform a Luttinger liquid ground state. We show that the spin spectral functionexhibits strong features representing the collective density and spin-wavemodes, which are broadened in an algebraic fashion with an exponentcharacterized by the Luttinger parameter. The possibilities of measuring thesecollective modes and detecting the power-law decay of the spectral weight usingNV relaxometry are discussed. We also examine how the transition rates aremodified by marginally irrelevant operators in the Heisenberg limit.

Detecting Fractionalization in Critical Spin Liquids using Color Centers