Low-dimensional fluctuations and pseudogap in Gaudin-Yang Fermi gases

Abstract

The pseudogap is a ubiquitous phenomenon in strongly correlated systems, such as high-T c superconductors, ultracold atoms, and nuclear physics. Whereas pairing fluctuations inducing the pseudogap are known to be enhanced in low-dimensional systems, such effects have not been explored well in one of the most fundamental one-dimensional models, that is, Gaudin-Yang model. In this paper, we show how the pseudogap effect emerges in the single-particle excitation in this system using a diagrammatic approach. Fermionic single-particle spectra exhibit a unique crossover from the double-particle dispersion to the pseudogap state with increasing the attractive interaction and the number density at finite temperature. Surprisingly, our results of thermodynamic quantities in unpolarized and polarized gases show an excellent agreement with the recent quantum Monte Carlo and complex Langevin results, indicating the validity of our approach even in the region where the pseudogap appears.

Unitary $p$-wave Fermi gas in one dimension

“…2. A similar spectral structure can be found in the case of the s-wave interaction in one dimension [70]. While the peak position in A(k, ω) at µ/T = 0 is close to the non-interacting dispersion ω = ξ k , at sufficiently large chemical potential where a pseudogap appears, deviation of the two branchs from the non-interacting dispersion increases with µ/T .…”

“…At larger µ, ρ(ω) shows the pseudogap opening around ω = 0 due to strong pairing fluctuations. Although emergence of a pseudogap is still under debate in a three-dimensional unitary Fermi gas [73,74], the present system is expected to have a pseudogap pairing enhanced by low-dimensional fluctuations [70]. We note that a possible pseudogap in a three-dimensional Fermi gas with p-wave interaction has also been discussed in Ref.…”

“…ν approaches zero in the large Λ limit. This is in contrast to the s-wave case where the coupling constant is finite and therefore the Hartree shift gives a nonzero contribution [70].…”

Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

“…It is also important to note here that in sharp contrast to higher spatial dimensions, the coupling constant g 1D does not vanish when Λ → ∞ in the renormalization procedure; see Section 2.1. Thus, we take the Hartree shift Σ H σ = g 1D N −σ into account in the building block of the self-energy diagrams [103]. This treatment is not necessary in the single-polaron limit since Σ H ↑ → 0 and…”

Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

“…II A. Thus, we take the Hartree shift Σ H σ = g 1D N −σ into account in the building block of the self-energy diagrams [94]. This treatment is not necessary in the single-polaron limit since Σ H ↑ → 0 and Σ H ↓ → g 1D T p,iωn G 0 ↑ (p, iω n ) (which is included in the TMA self-energy) when x → 0.…”