Entanglement Randomness and Gapped Itinerant Carriers in a Frustrated Quantum Magnet

The quantum spin liquid (QSL) is a state manifesting extraordinary many-body entanglement, and the material NaYbSe${}_2$ is thought to be one of the most promising candidates for its realization. Through low-temperature heat capacity and thermal conductivity measurements we identify an apparent contradiction familiar to many QSL candidates: while entropy is stored by apparently gapless excitations, the itinerant carriers of entropy are gapped. By studying the compositional series NaYb${}_x$Lu${}_{1-x}$Se${}_2$ across a percolation transition of the magnetic lattice, we suggest that this contradiction can be resolved by the presence of entanglement scales of random sizes. Moreover, as we truncate the scale of entanglement by magnetic dilution, we show that the itinerant magnetic entropy carrier in NaYb${}_x$Lu${}_{1-x}$Se${}_2$ is not the result of long-range entanglement but rather depends on the propagation of the simplest entangled object of all: the spin dimer.