Density-Induced Breaking of Pairs in the Attractive Hubbard Model

Abstract

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 < 0.18. 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=0.19. A pairing-induced pseudogap in the single-particle density of states is found at low densities and temperatures.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. Let

BCS-BEC crossover at finite temperature in the broken-symmetry phase

“…The approach developed in this subsection holds specifically for the approximate choice for the self-energy of Eq. (17). It thus differs from the general analysis presented in the Appendix which holds for the exact Green's functions, irrespective of any specific approximation.…”

“…(20) below]. In the Dyson's equation (17), however, µ is left unchanged since the constant shift Σ 0 is already contained in Σ 11 (k) as soon as its k-dependence is irrelevant. Accordingly, we have included this constant shift in the calculation of both thermodynamic and dynamical quantities in the weak-coupling side for (k F a F ) −1 ≤ −0.5, and neglected it for larger couplings when Σ 11 (k) can no longer be approximated by a constant.…”

“…(17). To this end, we need to perform the analytic continuation in the complex frequency plane, thus determining the retarded fermionic single-particle Green's functions from their Matsubara counterparts.…”

“…III. To this end, it is necessary to prove that the sum rule (A6) holds even for our approximate theory based on the Dyson's equation (17).…”

Transport properties calculation in the superconducting state for a quasi-two-dimensional system

“…In this paper we focused on the calculation of the Green function directly on the real frequency axis [16] in order to avoid the difficulties of controlling the accuracy of the calculations used in the numerical analytical continuations from the imaginary to the real axis by Padé algorithm [17]. In the previous paper [14] we presented the self-consistent equations set, which must be solved in order to obtain the Green function in the normal state.…”