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arXiv · 1710.08742

Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model

Song Cheng·Yu-Zhu Jiang·Yi-Cong Yu·Murray T. Batchelor·Xi-Wen Guan
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Abstract

We study the long-distance asymptotic behavior of various correlation functions for the one-dimensional (1D) attractive Hubbard model in a partially polarized phase through the Bethe ansatz and conformal field theory approaches. We particularly find the oscillating behavior of these correlation functions with spatial power-law decay, of which the pair (spin) correlation function oscillates with a frequency $Δk_F$ ($2Δk_F$). Here $Δk_F=π(n_\uparrow-n_\downarrow)$ is the mismatch in the Fermi surfaces of spin-up and spin-down particles. Consequently, the pair correlation function in momentum space has peaks at the mismatch $k=Δk_F$, which has been observed in recent numerical work on this model. These singular peaks in momentum space together with the spatial oscillation suggest an analog of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in the 1D Hubbard model. The parameter $β$ representing the lattice effect becomes prominent in critical exponents which determine the power-law decay of all correlation functions. We point out that the backscattering of unpaired fermions and bound pairs within their own Fermi points gives a microscopic origin of the FFLO pairing in 1D.

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Song Cheng, Yu-Zhu Jiang, Yi-Cong Yu, Murray T. Batchelor, Xi-Wen Guan. 2018-03-08. Asymptotic correlation functions and FFLO signature for the one-dimensional attractive Hubbard model. https://doi.org/10.1016/j.nuclphysb.2018.02.016

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