Simulating local measurements on a quantum many body system with stochastic matrix product states

Abstract

We demonstrate how to simulate both discrete and continuous stochastic evolution 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 anti-ferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular we focus on local measurements with small support and non-local measurements which induces long range correlations.

7 pages, 7 figures

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• Creation and dynamics of remote spin-entangled pairs in the expansion of strongly correlated fermions in an optical lattice
• Interacting spins in a cavity: finite size effects and symmetry-breaking dynamics
• Monte Carlo matrix-product-state approach to the false vacuum decay in the monitored quantum Ising chain
• Conditioned quantum motion of an atom in a continuously monitored 1D lattice