Optimal multi-configuration approximation of an N-fermion wave function

TL;DR

This paper introduces an iterative algorithm for optimally approximating an N-fermion wave function with multiple configurations, enhancing the study of entanglement and dynamics in multi-fermion systems.

Contribution

The paper presents a simple, convergent, and parallelizable algorithm for multi-configuration approximation of N-fermion wave functions, with applications to entanglement analysis and time-dependent simulations.

Findings

Algorithm converges monotonically

Effective in studying fermionic entanglement

Applied to ground state and dynamics of spinless fermions

Abstract

We propose a simple iterative algorithm to construct the optimal multi-configuration approximation of an $N$-fermion wave function. That is, $M\geq N $ single-particle orbitals are sought iteratively so that the projection of the given wave function in the $C_M^N$-dimensional configuration subspace is maximized. The algorithm has a monotonic convergence property and can be easily parallelized. The significance of the algorithm on the study of entanglement in a multi-fermion system and its implication on the multi-configuration time-dependent Hartree-Fock (MCTDHF) are discussed. The ground state and real-time dynamics of spinless fermions with nearest-neighbor interactions are studied using this algorithm, discussing several subtleties.