Simulating open quantum many-body systems using matrix product state purifications

Although we usually try to isolate quantum systems in the lab as effectively as possible, some degree of external noise and interaction with the environment is inevitable. This generally leads to decoherence, dissipation, and can alter the critical behavior in many-body systems. One can also try to engineer the environment coupling to achieve new physical phenomena. We consider Markovian systems, evolving according to Lindblad master equations. We introduce a new algorithm based on matrix product state purifications to simulate open many-body systems. This resolves a fundamental problem in simulations using matrix product density operators (MPDO) which generally lose positivity in truncations, leading to nonphysical states. We test and demonstrate our algorithm for spin chains and fermionic systems, comparing to exact diagonalization, analytical solutions, and MPDO simulations.