A Pilot-Wave Approach to the Many-Body Problem: Beyond the Small Entanglement Approximation

The de Broglie–Bohm pilot-wave theory provides an illuminating candidate solution to the philosophical problems that plague orthodox quantum theory. But the pilot-wave theory also has the potential to be of practical use to, for example, quantum chemists and condensed matter physicists who study many-body problems. In particular, the proprietary pilot-wave concept of the “conditional wave function” provides a novel perspective on and justification for a standard approach to many-body quantum systems in which the N-particle wave function is replaced by N single-particle wave functions. Moreover, this uniquely Bohmian “small entanglement approximation” (SEA) can be understood as the most basic level in a hierarchy of well-defined approximation schemes. Here we explain all of this theoretical background and then explore several of these approximation schemes (the SEA and beyond) numerically in the context of a simple toy model system.