Probing Pairing in Many-Body States with Particle Entanglement

In quantum many-body systems, particle pairing plays a key role in the emergence of collective quantum phases without classical analogues such as superfluidity and superconductivity. For fermions, the existence of the Pauli exclusion principle necessitates pairing before condensation can occur, with the resulting pairs exhibiting bosonic characteristics. In the presence of competing interactions or frustration, multiple paired phases are possible, including those with finite momentum or nodes in the pairing amplitude. Diagnosing the most energetically favorable pairing channel in a given system requires investigating an exhaustive list of hand-constructed multi-point correlation functions. In this talk, we report on progress in systematically probing pairing in fermionic quantum many-body states through an analysis of the spectrum of the two-body reduced density matrix and its associated two-particle eigenstates. We find that large eigenvalues (greater than unity) are indicative of strongly paired states, with the corresponding pair-eigenstates being highly entangled under a particle bipartition. We apply our general analysis to a specific microscopic model exhibiting a crossover between weak and tightly bound pairs.