  We examine the ground-state phase diagram and thermal phase transitions in a
plaquettized fully frustrated bilayer spin-1/2 Heisenberg model. Based on a
combined analysis from sign-problem free quantum Monte Carlo simulations,
perturbation theory and free-energy arguments, we identify a first-order
quantum phase transition line that separates two competing quantum-disordered
ground states with dominant singlet formations on inter-layer dimers and
plaquettes, respectively. At finite temperatures, this line extends to form a
wall of first-order thermal transitions, which terminates in a line of thermal
critical points. From a perturbative approach in terms of an effective Ising
model description, we identify a quadratic suppression of the critical
temperature scale in the strongly plaquettized region. Based on free-energy
arguments we furthermore obtain the full phase boundary of the low-temperature
dimer-singlet regime, which agrees well with the quantum Monte Carlo data.

Strongly Correlated Electrons