Sign-Problem-Free Real-Time Quantum Monte Carlo Simulations of Open Interacting Electron Systems

Non-equilibrium quantum many-body systems and quantum circuits have recently garnered much attention due to applications ranging from engineering non-equilibrium states of matter in materials to quantum computing. However, simulating the real-time dynamics of quantum systems remains a fundamental challenge – here, the exponential complexity in system size and time is commonly disguised as entanglement growth in tensor network algorithms or a dynamical sign problem in quantum Monte Carlo methods, limiting numerical studies to small or low-dimensional systems. In contrast, we show that dissipation due to coupling to the environment can dramatically ameliorate this situation and "cure" the dynamical sign problem in a real-time auxiliary-field quantum Monte Carlo formulation of interacting electrons coupled to a bath. In this picture, simulations of the real-time evolution of interacting electron systems admit a rigorous lower bound for the average fermion sign as a function of dissipation rates and interactions, while remaining sign-problem-free with polynomial simulation complexity beyond a critical dissipation strength. To illustrate the utility of this approach, we investigate the Floquet dynamics of periodically-driven interacting electron systems with Markovian dissipation, characterize the computational complexity of simple dissipative lattice models with interactions, and chart extensions to Majorana fermions. Our results establish a new tool to simulate the real-time dynamics of strongly-interacting dissipative fermionic systems in two or three dimensions.