Fermi-volume anomaly in quartet condensates

Abstract

We investigate the relation between density and Fermi volume in a four-component Fermi system with quartet order. For a regular zero-temperature branch without pair order, we express the correction to the Fermi-volume count in terms of the response of the Luttinger-Ward functional to a phase winding of the quartet source. Its leading term is a weighted difference between four-particle and four-hole states. For a Gaussian vertex and parabolic dispersion, we find that the correction expands the Fermi volume in one dimension and contracts it in three dimensions in the parameter range studied. The sign in two dimensions depends on the momentum cutoff. We solve the one-dimensional Dyson equation at fixed density and compare the counting correction obtained from the Fermi points with that evaluated from the dressed spectra at low temperature. At fixed quartet amplitude and peak normalization of the vertex, the correction depends strongly on the vertex width, whereas the fermionic entropy changes little. We also examine the linear pairing response, which can limit the continuation of the unpaired branch to zero temperature.