Luther-Emery liquid in one-dimensional attractive Fermi gas
Abstract
One-dimensional (1D) interacting Fermi gases underpin a rich variety of quantum liquids, ranging from the Tomonaga-Luttinger liquid and the Fulde-Ferrell-Larkin-Ovchinnikov paired state to the Luther-Emery liquid (LEL). Notably, the LEL-characterized by gapless excitations in charge or spin degree of freedom and gapped excitations in the other-has long been theoretically predicted but has eluded definitive experimental observation to date. By exactly solving the attractive Yang-Gaudin model via the Bethe ansatz, we fully determine the low-energy excitation spectra for both spin and charge channels. For fully paired fermions, the spectrum features gapped spin excitation coexisting with gapless charge excitation. We further employ bosonization to derive analytical expressions for the dynamical structure factor (DSF) of the gapped spin excitation, which is a long-standing challenge in this study. In the trapped gas, we find that the spin Bragg spectroscopy peak occurs at a much higher frequency than the charge-mode peak, where the splitting frequency between these two peaks scales approximately linearly with the interaction strength. Crucially, the spin gap manifests as a sharp threshold in the spin DSF, below which spectral weight is completely absent, proving a direct and unambiguous spectroscopic fingerprint of the LEL. Our work establishes quasi-1D trapped attractive Fermi gases as a pristine experimental platform for the long-sought direct observation of the LEL.
Related
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BibTeX
@misc{cui2026lutheremery,
title = {{Luther-Emery liquid in one-dimensional attractive Fermi gas}},
author = {Hai-Ying Cui and Yi-Cong Yu and Aashish Kafle and Han Pu and Randall G. Hulet and Thierry Giamarchi and Xî-Wen Guan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27823},
eprint = {2610.27823},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27823},
}
RIS
TY - UNPB
TI - Luther-Emery liquid in one-dimensional attractive Fermi gas
AU - Hai-Ying Cui
AU - Yi-Cong Yu
AU - Aashish Kafle
AU - Han Pu
AU - Randall G. Hulet
AU - Thierry Giamarchi
AU - Xî-Wen Guan
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27823
UR - https://arxiv.org/abs/2610.27823
AB - One-dimensional (1D) interacting Fermi gases underpin a rich variety of quantum liquids, ranging from the Tomonaga-Luttinger liquid and the Fulde-Ferrell-Larkin-Ovchinnikov paired state to the Luther-Emery liquid (LEL). Notably, the LEL-characterized by gapless excitations in charge or spin degree of freedom and gapped excitations in the other-has long been theoretically predicted but has eluded definitive experimental observation to date. By exactly solving the attractive Yang-Gaudin model via the Bethe ansatz, we fully determine the low-energy excitation spectra for both spin and charge channels. For fully paired fermions, the spectrum features gapped spin excitation coexisting with gapless charge excitation. We further employ bosonization to derive analytical expressions for the dynamical structure factor (DSF) of the gapped spin excitation, which is a long-standing challenge in this study. In the trapped gas, we find that the spin Bragg spectroscopy peak occurs at a much higher frequency than the charge-mode peak, where the splitting frequency between these two peaks scales approximately linearly with the interaction strength. Crucially, the spin gap manifests as a sharp threshold in the spin DSF, below which spectral weight is completely absent, proving a direct and unambiguous spectroscopic fingerprint of the LEL. Our work establishes quasi-1D trapped attractive Fermi gases as a pristine experimental platform for the long-sought direct observation of the LEL.
ER -