Fermion Monte Carlo Algorithms for Quantum Fluids

Abstract

Accurate first-principles calculations of the macroscopic properties of quantum fluids from microscopic interactions remain a key focus of many-body theorists.1 Our approach can be presented in summary fashion by saying that we seek to solve the Schrodinger equation: $$ H\psi _0 = E\psi _0 $$ (1) to obtain the ground-state wave funetion ψ for a given Hamiltonian H whose energy eigen value is E. For anyone familiar with many-body approaehes to this problem , it is clear that we are presented with a problem of shocking proportions: we are seeking to solve one equation whieh has (at least) four unknowns: 1. We generally do not know the correct Hamiltonian which eorresponds to material reality. 2. We generally do not know in closed form the ground-state wave function. 3. We generally do not know the energy eigenvalue for the exact Hamiltonian. 4. We generally do not know how to proceed with the calculation of the many-dimensional integrals inherent in the problem. The history of where to begin and how to proceed with narrowing the number of unknowns in the problem, then, traces the history of many-body theory over the past half century.2