1p1h

1p1h, short for one-particle–one-hole excitation, is a fundamental configuration in many-body quantum mechanics. Starting from a reference state, typically a Slater determinant for a noninteracting or mean-field ground state, one particle is promoted from an occupied orbital i to an unoccupied orbital a. The resulting excited determinant is denoted |Φ_i^a> = c_a^† c_i |Φ0>, containing a hole in i and a particle in a in the same system. Energy in the independent-particle picture is about ε_a − ε_i; the residual two-body interaction couples many such configurations and yields correlated excited states.

1p1h configurations form the building blocks of linear response and excitation theories. The particle–hole propagator, assembled from 1p1h states, underpins methods such as the random phase approximation (RPA) and the Tamm-Dancoff approximation (TDA); TDHF is a time-dependent extension. These approaches describe collective modes such as giant resonances in nuclei and plasmons in solids as coherent superpositions of 1p1h excitations. In spectroscopy, charge and spin responses are interpreted in terms of transitions between occupied and unoccupied single-particle levels connected by 1p1h configurations. In many-body calculations, restricting to 1p1h space is a common approximation (e.g., in the TDA) that neglects more complex 2p2h and higher configurations, but it captures essential physics of small-amplitude and single-particle-like excitations.

While 1p1h is a simplified picture, it remains a convenient and widely used concept across nuclear, atomic, and solid-state physics for describing elementary excitations and as a stepping stone to more sophisticated theories.