nparticlenhole

Nparticlenhole, or n-particle-n-hole excitations, is a concept in many-body quantum physics used to describe correlated excited configurations where n particles are promoted from occupied orbitals to higher-lying virtual orbitals, leaving behind n holes in the reference ground state. The term is commonly shortened to npnh or np-nh in the literature.

Formally, in a system with a reference ground state represented by a Slater determinant |Φ0>, an npnh excitation is a determinant obtained by selecting occupied orbitals i1,...,in and virtual orbitals a1,...,an, and constructing |Φ_{i1...in}^{a1...an}> = c†_{a1}...c†_{an} c_{in}...c_{i1} |Φ0>. The simplest cases are 1p-1h, 2p-2h, and so on. These excitations form the configuration space used in configuration interaction (CI) calculations and related many-body methods.

In chemistry and nuclear physics, npnh excitations underpin descriptions of electron correlation and collective excitations. Truncated CI approaches allow calculations including up to kp-kh excitations (e.g., CISD includes up to 2p-2h). They are essential for capturing multi-particle correlations beyond single excitations, but the combinatorial growth of possible excitations makes full npnh spaces computationally challenging.

In practice, npnh spaces are often combined with selection schemes, perturbative corrections, or coupled-cluster methods that implicitly include certain high-order excitations. The concept helps categorize excitation effects by how many particles and holes participate, aiding interpretation of spectra and correlation energies.

Related concepts include particle-hole excitations and configuration interaction, as well as coupled-cluster theory and the nuclear shell model.