Real-Time Simulation of Large Open Quantum Spin Systems driven by Measurements

We consider a large quantum system with spins $\frac{1}{2}$ whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution of a 2-d Heisenberg antiferromagnet, which is driven to a disordered phase, either by sporadic measurements or by continuous monitoring described by Lindblad evolution.