Using quantum Monte Carlo to study quantum phase transitions

We derive a scheme to estimate fidelity susceptibility in permutation matrix representation quantum Monte Carlo (PMR-QMC) and test it numerically. Fidelity susceptibility is a universal indicator of quantum phase transitions, and hence, our work allows for the study of quantum phases even without knowledge of an underlying order parameter. We remark that previous works have derived similar schemes for imaginary time and stochastic series expansion QMC (Wang et. al. PhysRevX.5.031007). However, PMR-QMC is neither an imaginary time nor stochastic series expansion method, and hence, our scheme does not follow directly from previous work. Instead, PMR-QMC is a sampling scheme over permutations with weights given by divided differences of the Boltzmann exponential. The PMR-QMC has many benefits over imaginary time and stochastic series expansion methods (Lalit et. al. J. Stat. Mech. (2020) 073105]), so our scheme inherits all these benefits over previous approaches.