Natural Quantum Monte Carlo Computation of Excited States

Abstract

We present a variational Monte Carlo algorithm for estimating the lowest excited states of a quantum system which is a natural generalization of the estimation of ground states. The method requires no explicit orthogonalization of the different states, instead transforming the problem of finding excited states of a given system into that of finding the ground state of an expanded system. Expected values of arbitrary observables can be calculated, including mixed expectations between different states such as the transition dipole moment. Although the method is entirely general, it works particularly well in conjunction with recent work on using neural networks as variational Ansätze for many-electron systems, and we show that by combining this method with the FermiNet and Psiformer Ansätze we can accurately recover vertical excitation energies and oscillator strengths on molecules as large as benzene. Beyond the examples on molecules presented here, we expect this technique will be of great interest for applications of variational quantum Monte Carlo to atomic, nuclear and condensed matter physics.

Authors

David Pfau, Simon Axelrod*, Halvard Sutterud*, James Spencer, Ingrid von Glehn

Venue

arXiv