Efficient implementation of the Projection Operator Imaginary Time Spectral Evolution (POITSE) method for excited states

We describe and systematically analyze new implementations of the Projection Operator Imaginary Time Spectral Evolution (POITSE) method for the Monte Carlo evaluation of excited state energies. The POITSE method involves the computation of a correlation function in imaginary time. Decay of this function contains information about excitation energies, which can be extracted by a spectral transform. By incorporating branching processes in the Monte Carlo propagation, we compute these correlation functions with significantly reduced statistical noise. Our approach allows for the stable evaluation of small energy differences in situations where the previous POITSE implementation was limited by this noise.