Released-phase quantum Monte Carlo method

The correlation function Monte Carlo method for calculating ground and excited state properties is extended to complex Hamiltonians and used to calculate the spectrum of neutral helium in a wide range of magnetic fields, a system of particular interest in astrophysics. Correlation functions in imaginary time are evaluated for a set of trial functions over a random walk whose dynamics is governed by the imaginary-time Schrödinger equation. Estimates of the exact energy spectrum and other expectations are made by diagonalizing the matrix of correlation functions. Using the exact results of this “released-phase” Monte Carlo approach, we assess the accuracy of the fixed-phase quantum Monte Carlo and Hartree-Fock methods for the helium atom in strong magnetic fields.