Advanced measurement techniques in quantum Monte Carlo: The permutation matrix representation approach

Abstract: In a typical finite temperature quantum Monte Carlo (QMC) simulation, estimators for simple static observables such as specific heat and magnetization are known. With a great deal of system-specific manual labor, one can sometimes also derive more complicated non-local or even dynamic observable estimators. Within the permutation matrix representation (PMR) flavor of QMC, however, we show that one can derive formal estimators for arbitrary static observables. We also derive exact, explicit estimators for general imaginary-time correlation functions and non-trivial integrated susceptibilities thereof. We demonstrate the practical versatility of our method by estimating various non-local, random observables for the transverse-field Ising model on a square lattice.