Spin liquid regimes at nonzero temperature in quantum spin ice

Quantum spin liquids are highly entangled ground states of quantum systems with an emergent gauge structure, fractionalized spinon excitations, and other unusual properties. While these features clearly distinguish quantum spin liquids from conventional, mean-field-like states at zero temperature ($T$), their status at $T>0$ is less clear. Strictly speaking, it is known that most quantum spin liquids lose their identity at nonzero temperature, being then adiabatically transformable into a trivial paramagnet. This is the case for the $U\left(1\right)$ quantum spin liquid states recently proposed to occur in the quantum spin ice pyrochlores. Here we propose, however, that in practical terms, the latter quantum spin liquids can be regarded as phases distinct from the high-temperature paramagnet. Through a combination of gauge mean-field theory calculations and physical reasoning, we argue that these systems sustain both quantum spin liquid and thermal spin liquid phases, dominated by quantum fluctuations and entropy, respectively. These phases are separated by a first-order “thermal confinement” transition such that, for temperatures below the transition, spinons and emergent photons are coherently propagating excitations, and above it the dynamics is classical. Even for parameters for which the ground state is magnetically ordered and not a quantum spin liquid, this strong first-order transition occurs, preempting conventional Landau-type criticality. We argue that this picture explains the anomalously low-temperature phase transition observed in the quantum spin ice material Yb${}_2$Ti${}_2$O${}_7$.