Efficient exact diagonalization of the n-body reduced density matrix

The n-body reduced density matrix provides an alternate description of a quantum-many body system that can offer considerable compression over the wavefunction while providing access to observables and correlation functions. In this talk, we present an efficient algorithm for its construction and exact diagonalization in a system of N interacting particles. In one spatial dimension, we simplify computations by exploiting translational, reflection and particle-hole symmetries. We illustrate the method by calculating the maximal particle entanglement entropy constructed from the N/2-particle reduced density matrix in the ground state of up to 13 interacting fermions on 26 sites.