Thermodynamics of a gauge-frustrated Kitaev spin liquid

Two- and three-dimensional Kitaev magnets are prototypical frustrated quantum spin systems, in which the original spin degrees of freedom fractionalize into Majorana fermions and a $\mathbb{Z}_2$ gauge field -- a purely local phenomenon that reveals itself as a thermodynamic crossover at a temperature scale set by the strength of the bond-directional interactions. For conventional Kitaev magnets, the low-temperature thermodynamics reveals a second transition at which the $\mathbb{Z}_2$ gauge field orders and the system enters a spin liquid ground state. Here we discuss an explicit example that goes beyond this paradigmatic scenario -- the $\mathbb{Z}_2$ gauge field is found to be subject to geometric frustration, the thermal ordering transition is suppressed, and an extensive residual entropy arises. Deep in the quantum regime, at temperatures of the order of one per mil of the interaction strength, the degeneracy in the gauge sector is lifted by a subtle interplay between the gauge field and the Majorana fermions, resulting in the formation of a Majorana metal. We discuss the thermodynamic signatures of this physics obtained from large-scale, sign-free quantum Monte Carlo simulations.