Partial flux ordering and thermal Majorana metals in higher-order spin liquids

In frustrated quantum magnetism, chiral spin liquids are a particularly intriguing subset of quantum spin liquids in which the fractionalized parton degrees of freedom form a Chern insulator. Here we study an exactly solvable spin-3/2 model, which harbors not only chiral spin liquids but also spin liquids with higher-order parton band topology - a trivial band insulator, a Chern insulator with gapless chiral edge modes, and a second-order topological insulator with gapless corner modes. With a focus on the thermodynamic precursors and thermal phase transitions associated with these distinct states, we employ numerically exact quantum Monte Carlo simulations to reveal a number of unconventional phenomena. This includes heightened thermal stability of the ground state phases, the emergence of a partial flux ordering of the associated Z2 lattice gauge field, and the formation of a thermal Majorana metal regime extending over a broad temperature range.