Asymptotic correlation functions and FFLO signature for the one-dimensional attractive spin-1/2 Fermi gas

Abstract

We investigate the long distance asymptotics of various correlation functions for the one-dimensional spin-1/2 Fermi gas with attractive interactions using the dressed charge formalism. In the spin polarized phase, these correlation functions exhibit spatial oscillations with a power-law decay whereby their critical exponents are found through conformal field theory. We show that spatial oscillations of the leading terms in the pair correlation function and the spin correlation function solely depend on $\Delta k_F$ and $2\Delta k_F$, respectively. Here $\Delta k_F=\pi (n_{\uparrow }-n_{\downarrow })$ denotes the mismatch between the Fermi surfaces of spin-up and spin-down fermions. Such spatial modulations are characteristics of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Our key observation is that backscattering among the Fermi points of bound pairs and unpaired fermions results in a one-dimensional analog of the FFLO state and displays a microscopic origin of the FFLO nature. Furthermore, we show that the pair correlation function in momentum space has a peak at the point of mismatch between both Fermi surfaces $k=\Delta k_F$, which has recently been observed in numerous numerical studies.

2 figures, 18 pages

References in corpus (11)

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Cited by in corpus (19)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
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• Expansion of 1D polarized superfluids: The FFLO state reveals itself
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Dimer, trimer and FFLO liquids in mass- and spin-imbalanced trapped binary mixtures in one dimension
• Wilson ratio of Fermi gases in one dimension
• Thermodynamics, spin-charge separation and correlation functions of spin-1/2 fermions with repulsive interaction
• Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases
• Critical phenomena in one dimension from a Bethe ansatz perspective
• Enhanced visibility of the Fulde-Ferrell-Larkin-Ovchinnikov state in one dimensional Bose-Fermi mixtures near the immiscibility point
• Dimensional Crossover in a Spin-imbalanced Fermi gas
• FFLO correlation and free fluids in the one-dimensional attractive Hubbard model
• Pure Fulde-Ferrell-Larkin-Ovchinnikov state in optical lattices
• Exotic pairing in 1D spin-3/2 atomic gases with $SO(4)$ symmetry
• Nesting and lifetime effects in the FFLO state of quasi-one-dimensional imbalanced Fermi gases
• Spin-imbalanced ultracold Fermi gases in a two-dimensional array of tubes
• Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model
• Trapped imbalanced fermionic superfluids in one dimension: A variational approach
• In-medium bound-state formation and inhomogeneous condensation in Fermi gases in a hard-wall box