  Quantum spin liquids are highly entangled ground states of quantum systems
with 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 non-zero temperature, being in that
case adiabatically transformable into a trivial paramagnet. This is the case
for the U(1) 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 distinct phases 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, pre-empting conventional Landau-type
criticality. We argue that this picture explains the anomalously low
temperature phase transition observed in the quantum spin ice material
Yb2Ti2O7.
