1 Department of Physics and Astronomy, Faculty of Science, Aarhus University, Aarhus University2 Teoretisk naturvidenskab, Aarhus University, Aarhus University3 Department of Physics and Astronomy, Science and Technology, Aarhus University4 Department of Physics and Astronomy, Science and Technology, Aarhus University
We demonstrate how to simulate both discrete and continuous stochastic evolutions of a quantum many-body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators is found. The technique is exemplified by numerical simulations of the antiferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular, we focus on local measurements with small support and nonlocal measurements, which induce long-range correlations.