Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Low Temperature Physics

Exact Analysis of a One-Dimensional Attractive δ-Function Fermi Gas with Arbitrary Spin Polarization

Toshiaki Iida, Miki Wadati

Published May 29, 2007• 3 citations
Publisher
DOI
10.1007/s10909-007-9409-7

Related papers

Onset of magnetization in the one-dimensional Fermi gas with attractive δ -function potential

P. Schlottmann

Journal of Magnetism and Magnetic Materials•Apr 25, 2024•0 citations

Exact analysis of a δ-function spin-1/2 attractive Fermi gas with arbitrary polarization

Toshiaki Iida, Miki Wadati

The ground state of a one-dimensional δ-function attractive spin-1/2 fermions is studied by the nested Bethe ansatz method. Explicitly, the Gaudin integral equation for the system is solved in the form of power series with arbitrary spin polarization. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. The physical quantities, such as the ground state energy and the chemical potentials, are expressed in terms of the dimensionless coupling constant and the polarization , where c is the coupling constant and are the number densities of the spin-up (down) particles. While in the limiting case P = 1, the system consists of spinless free fermions, the other limit P = 0 describes the BCS–BEC crossover in one dimension. As a function of P , the evolution is continuous and smooth.

Journal of Statistical Mechanics Theory and Experiment•Jun 14, 2007•21 citations

One-dimensional Spin-polarized Fermi Gas near resonances

Yuta Sekino, Yusuke Nishida

Bulletin of the American Physical Society•Mar 2, 2020•0 citations

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interaction

Xi‐Wen Guan

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.

arXiv:1202.2941•Frontiers of Physics•Nov 4, 2011•23 citations

An Effective Field Theory for One-dimensional Polarized Fermi Gases

Erhai Zhao, W. Vincent Liu

Journal of Low Temperature Physics•Sep 2, 2009•8 citations

Exact Analysis of a δ-Function Spin-1/2 Attractive Fermi Gas with an External Magnetic Field

Toshiaki Iida, Miki Wadati

We study the excitation spectrum of a one-dimensional δ-function attractive spin-1/2 fermions by the thermal Bethe ansatz method at zero temperature. The integral equation for the dressed energies of the system with an external magmatic field is solved in the form of power series. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. We also study the magnetization as a function of the coupling constant and the external field.

Journal of the Physical Society of Japan•Feb 12, 2008•24 citations
The ground state of a one-dimensional δ-function attractive spin-1/2 fermions is studied by the nested Bethe ansatz method. Explicitly, the Gaudin integral equation for the system is solved in the form of power series with arbitrary spin polarization. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. The physical quantities, such as the ground state energy and the chemical potentials, are expressed in terms of the dimensionless coupling constant and the polarization , where c is the coupling constant and are the number densities of the spin-up (down) particles. While in the limiting case P = 1, the system consists of spinless free fermions, the other limit P = 0 describes the BCS–BEC crossover in one dimension. As a function of P , the evolution is continuous and smooth.
Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.