Thermal Critical Points and Quantum Critical End Point in the Frustrated Bilayer Heisenberg Antiferromagnet

We present a quantum Monte Carlo scheme for the simulation of frustrated quantum magnets that allows us to reduce or even eliminate the spin-problem for several dimerized quantum spin systems. We discuss in particular its application to the thermal properties of the spin-1/2 Heisenberg model on a frustrated square lattice bilayer. At zero temperature for the later model, a discontinuous quantum phase transition separates an interlayer singlet phase from an antiferromagnetic ground state formed by interlayer triplets. We show that this discontinuous transition extends up to finite temperatures and terminates in a quantum critical point. We identify this critical point as belonging to the Ising universality class, alert long-range order being absent at finite temperatures. We furthermore trace the discontinuous quantum phase transitions between the fully frustrated and the unfrustrated bilayer model using iPEPS tensor network methods. In particular, we identify a quantum critical end point that terminates the quantum critical line originating from the critical point of the unfrustrated bilayer system on the discontinuous transition line.