Fixed-node and fixed-phase approximations and their relationship to variable spins in quantum Monte Carlo

TL;DR

This paper compares fixed-node and fixed-phase approximations in quantum Monte Carlo, showing their similarities and differences, and introduces a new formalism for fully quantum spin-spatial wave functions to improve fermionic system simulations.

Contribution

It provides a detailed comparison of fixed-node and fixed-phase methods and introduces a novel formalism for wave functions with full antisymmetry in spin-spatial degrees of freedom.

Findings

Fixed-phase and fixed-node behave similarly with high-accuracy nodes/phase.

Fixed-phase shows larger biases with large trial wave function errors.

New formalism allows fully quantum spin-spatial wave functions for fermionic systems.

Abstract

We compare the fixed-phase approximation with the better known, but closely related fixed-node approximation on several testing examples. We found that both approximations behave very similarly with the fixed-phase results being very close to the fixed-node method whenever nodes/phase were of high and comparable accuracy. The fixed-phase exhibited larger biases when the trial wave functions errors in the nodes/phase were intentionally driven to unrealistically large values. We also present a formalism that enables to describe wave functions with the full antisymmetry in spin-spatial degrees of freedom using our recently developed method for systems with spins as fully quantum variables. This opens new possibilities for simulations of fermionic systems in the fixed-phase approximation formalism.