A Monte Carlo algorithm for calculating the overlap between ground states

Gaining insight into the overlap between the respective ground states of two given Hamiltonians has become increasingly important in recent years This need arises in various contexts, including the detection of quantum phase transitions, the study of the Anderson orthogonality catastrophe, and the exploration of critical systems. Additionally, this concept plays a pivotal role in the realm of quantum quenches involving impurity systems. I will discuss a novel Monte Carlo algorithm for calculating the overlap between the ground states of two input quantum Hamiltonians and share some results demonstrating the applicability and scope of the technique.