Long-time evolution of quantum systems with Tensor Network techniques

Abstract

One of the most significant challenges in simulating the dynamics of manybody quantum systems is the exponential increase in computational complexity, driven by the linear growth of entanglement during time evolution. In this work, we explore a novel algorithm designed to mitigate this complexity by identifying and trading the entanglement by mixture, i.e. depurifying the originally pure closed-system state. This approach preserves the essential local information necessary for computing expectation values, while effectively reducing the computational resources. Additionally, we propose a method for performing time evolution with the resulting mixed states, highlighting both the strengths and limitations of this approach. We also discuss potential avenues for future improvements to enhance the efficiency and applicability of this method.