How many bodies are many-body? Characterizing the effect of lattice sizes on many-body entanglements through thermal conductivity measurements on NaYb_xLu_1-xSe₂

Quantum spin liquid (QSL) is an intriguing many-body phase of matter characterized by its anomalously high degree of entanglement. While new crystal candidates hosting QSL are synthesized continually, in recent years, simulating QSLs with Rydberg-atom-array-based quantum simulators [Semeghini 2021] has gained considerable momentum. To characterize such an inherently many-body phase as QSL, infinitely large lattices of perfect geometric order are needed theoretically. In experimental practices, however, quantum simulators are limited to a few hundred sites, and lattice disorders are inevitable in crystal growths. Both limitations could drastically alter the intended QSL phases simulated or hosted [de la Torre 2023]. Therefore, it is crucial to investigate how lattice size and boundary conditions would affect the formation of QSL, attempting to answer the fundamental question of “how many bodies are many-body?” To do this, we synthesized compositions of NaYb_xLu_1-xSe₂, where by increasing the doping x, we can form a collection of antiferromagnetic triangular lattices of Jeff = 1/2 Yb³⁺ ions with growing sizes and connections. We then characterize this series via thermal transport measurements under extremely low temperatures, focusing on the behavior changes across the percolation transition at x = 0.5 when isolated lattices join to form networks of infinity size.