Density-Induced Breaking of Pairs in the Attractive Hubbard Model

A conserving $T$-matrix approximation is applied to the two-dimensional attractive Hubbard model in the low-density regime. A set of self-consistent equations is solved in the real-frequency domain to avoid the analytic continuation procedure. By tuning the chemical potential the particle density was varied in the limits $0.01<n<\mathrm{}0.18\mathrm{}$. For the value of the attractive potential $U=8t$ the binding energy of pairs monotonically decreases with increasing $n$, from its zero-density limit $2.3t$, and vanishes at a critical density $n_{\mathrm{cr}}=0.19\mathrm{}$. A pairing-induced pseudogap in the single-particle density of states is found at low densities and temperatures.