Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices

Abstract By using the exact Bethe wavefunctions of the one-dimensional Hubbard model with N spin-up fermions and one spin-down impurity, we derive an analytic expression of the impurity form factor, in the form of a determinant of a $$(N+1)$$ ( N + 1 ) by $$(N+1)$$ ( N + 1 ) matrix. This analytic ex...

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Main Authors: Xia-Ji Liu, Hui Hu
Format: Article
Language:English
Published: Springer 2025-03-01
Series:AAPPS Bulletin
Online Access:https://doi.org/10.1007/s43673-025-00149-7
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author Xia-Ji Liu
Hui Hu
author_facet Xia-Ji Liu
Hui Hu
author_sort Xia-Ji Liu
collection DOAJ
description Abstract By using the exact Bethe wavefunctions of the one-dimensional Hubbard model with N spin-up fermions and one spin-down impurity, we derive an analytic expression of the impurity form factor, in the form of a determinant of a $$(N+1)$$ ( N + 1 ) by $$(N+1)$$ ( N + 1 ) matrix. This analytic expression enables us to exactly calculate spectral properties of one-dimensional Fermi polarons in lattices, when the masses of the impurity particle and the Fermi bath are equal. We present the impurity spectral function as functions of the on-site interaction strength and the filling factor of the Fermi bath, and discuss the origin of Fermi singularities in the spectral function at small momentum and the emergence of polaron quasiparticles at large momentum near the boundary of Brillouin zone. Our analytic expression of the impurity form factors pave the way to exploring the intriguing dynamics of a particle interacting with a Fermi bath. Our exact predictions on the impurity spectral function could be directly examined in cold-atom laboratories by using the radio-frequency spectroscopy and Ramsey spectroscopy.
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publisher Springer
record_format Article
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spelling doaj-art-90e42ea152dc48ef86b612509723fa852025-08-20T01:56:09ZengSpringerAAPPS Bulletin2309-47102025-03-0135111610.1007/s43673-025-00149-7Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical latticesXia-Ji Liu0Hui Hu1Centre for Quantum Technology Theory, Swinburne University of TechnologyCentre for Quantum Technology Theory, Swinburne University of TechnologyAbstract By using the exact Bethe wavefunctions of the one-dimensional Hubbard model with N spin-up fermions and one spin-down impurity, we derive an analytic expression of the impurity form factor, in the form of a determinant of a $$(N+1)$$ ( N + 1 ) by $$(N+1)$$ ( N + 1 ) matrix. This analytic expression enables us to exactly calculate spectral properties of one-dimensional Fermi polarons in lattices, when the masses of the impurity particle and the Fermi bath are equal. We present the impurity spectral function as functions of the on-site interaction strength and the filling factor of the Fermi bath, and discuss the origin of Fermi singularities in the spectral function at small momentum and the emergence of polaron quasiparticles at large momentum near the boundary of Brillouin zone. Our analytic expression of the impurity form factors pave the way to exploring the intriguing dynamics of a particle interacting with a Fermi bath. Our exact predictions on the impurity spectral function could be directly examined in cold-atom laboratories by using the radio-frequency spectroscopy and Ramsey spectroscopy.https://doi.org/10.1007/s43673-025-00149-7
spellingShingle Xia-Ji Liu
Hui Hu
Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices
AAPPS Bulletin
title Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices
title_full Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices
title_fullStr Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices
title_full_unstemmed Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices
title_short Exact calculation of spectral properties of a particle interacting with a one-dimensional Fermi gas in optical lattices
title_sort exact calculation of spectral properties of a particle interacting with a one dimensional fermi gas in optical lattices
url https://doi.org/10.1007/s43673-025-00149-7
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