Entanglement Randomness and Gapped Itinerant Carriers in a Frustrated Quantum Magnet

The quantum spin liquid is a state manifesting extraordinary many-body entanglement, and the material <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>NaYbSe</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> 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 quantum spin liquid candidates: While entropy is stored by apparently gapless excitations, the itinerant carriers of entropy are gapped. By studying the compositional series <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>NaYb</c:mi> </c:mrow> <c:mrow> <c:mi>x</c:mi> </c:mrow> </c:msub> </c:mrow> <c:mrow> <c:msub> <c:mrow> <c:mi>Lu</c:mi> </c:mrow> <c:mrow> <c:mn>1</c:mn> <c:mo>−</c:mo> <c:mi>x</c:mi> </c:mrow> </c:msub> <c:mrow> <c:msub> <c:mrow> <c:mi>Se</c:mi> </c:mrow> <c:mrow> <c:mn>2</c:mn> </c:mrow> </c:msub> </c:mrow> </c:mrow> </c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msub> <e:mrow> <e:mi>NaYbSe</e:mi> </e:mrow> <e:mrow> <e:mn>2</e:mn> </e:mrow> </e:msub> </e:mrow> </e:math> does not arise from a uniform globally entangled spin ground state but rather materializes through the stochastic propagation of boundaries between locally entangled spin objects.