In this Rapid Communication, we investigate the universal properties of a spin-polarized two-component Fermi gas in one dimension (1D) using the Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility, and the contact susceptibility, giving a precise understanding of the 1D analog of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimensions (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility $\ensuremath{\chi}\ensuremath{\sim}1/\sqrt{T}exp(\ensuremath{-}\mathrm{\ensuremath{\Delta}}/T)$ at low temperatures, where $\mathrm{\ensuremath{\Delta}}$ is the energy gap and $T$ is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization $P$ and the contact $C$ for both repulsive and attractive Fermi gases. Our findings emphasize the role of pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.In this Rapid Communication, we investigate the universal properties of a spin-polarized two-component Fermi gas in one dimension (1D) using the Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility, and the contact susceptibility, giving a precise understanding of the 1D analog of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimensions (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility $\ensuremath{\chi}\ensuremath{\sim}1/\sqrt{T}exp(\ensuremath{-}\mathrm{\ensuremath{\Delta}}/T)$ at low temperatures, where $\mathrm{\ensuremath{\Delta}}$ is the energy gap and $T$ is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization $P$ and the contact $C$ for both repulsive and attractive Fermi gases. Our findings emphasize the role of pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.

arXiv:1603.07207Physical Review ASep 21, 201612 citations

Heavy Fermi polarons in a one-dimensional harmonic trap

Nikolay Yegovtsev

We provide an analytically tractable toy model of an infinitely heavy impurity interacting with the spin-polarized gas of bath fermions via a contact potential in 1D and placed in a harmonic trap. The solution to this problem requires knowledge of the single-particle fermionic eigenstates in the presence of a harmonic trap and a contact potential. We show how the spectrum can be understood from a perturbative solution of the exact transcendental equation in the weak and strong-coupling regimes. We additionally provide expressions for normalized wavefunctions and different overlaps between the states in the presence and absence of the impurity. Using these exact results, we analyze the energy of the polaron, derive Tan's contact-like relation for the density at the center of the harmonic trap, and compute the quasiparticle residue.We provide an analytically tractable toy model of an infinitely heavy impurity interacting with the spin-polarized gas of bath fermions via a contact potential in 1D and placed in a harmonic trap. The solution to this problem requires knowledge of the single-particle fermionic eigenstates in the presence of a harmonic trap and a contact potential. We show how the spectrum can be understood from a perturbative solution of the exact transcendental equation in the weak and strong-coupling regimes. We additionally provide expressions for normalized wavefunctions and different overlaps between the states in the presence and absence of the impurity. Using these exact results, we analyze the energy of the polaron, derive Tan's contact-like relation for the density at the center of the harmonic trap, and compute the quasiparticle residue.

arXiv:2509.01934Sep 2, 20250 citations

One-dimensional spin-polarized fermions

Anna Minguzzi

Bulletin of the American Physical SocietyMar 16, 20060 citations

Spectroscopy and the nature of the ground state of trapped polarized fermions

Erich J. Mueller

Nov 1, 20070 citations

Tan's Contact for Trapped Spin-Orbit-Coupled Fermi Gases at Finite Temperature

Tianhao Wu, Yuanbang Wei, Rui Tian +7 more

Tan's contact, bridging microscopic features of many-body quantum systems to two-body contact interactions, is pivotal in the description of quantum gases. However, past studies of Tan's contact of the spin-orbit coupled Fermi gases have been exclusively discussed at zero temperature. The thermal effects on that, which cannot be neglected in most experimental conditions, has not been explored so far. Here, through a path integral Monte Carlo (PIMC) study, we show that thermal effects fundamentally alter the scaling relation between spin-orbit coupling (SOC) and Tan's contact. The linear scaling of Tan's contact with respect to the strength of SOC found at zero temperature is drastically undermined by the thermal effects. And a new mechanism based on the competition between the mean occupancy and the energy-reweighted occupancy of the opposite spin fermion pairs within the interaction range has been unveiled, which radically changes the above linear scaling to a non-monotonic dependence. Our work should be useful for future experiments to explore the preternatural thermal effects on Tan's contact of the strongly interacting spin-orbit-coupled Fermi gas.Tan's contact, bridging microscopic features of many-body quantum systems to two-body contact interactions, is pivotal in the description of quantum gases. However, past studies of Tan's contact of the spin-orbit coupled Fermi gases have been exclusively discussed at zero temperature. The thermal effects on that, which cannot be neglected in most experimental conditions, has not been explored so far. Here, through a path integral Monte Carlo (PIMC) study, we show that thermal effects fundamentally alter the scaling relation between spin-orbit coupling (SOC) and Tan's contact. The linear scaling of Tan's contact with respect to the strength of SOC found at zero temperature is drastically undermined by the thermal effects. And a new mechanism based on the competition between the mean occupancy and the energy-reweighted occupancy of the opposite spin fermion pairs within the interaction range has been unveiled, which radically changes the above linear scaling to a non-monotonic dependence. Our work should be useful for future experiments to explore the preternatural thermal effects on Tan's contact of the strongly interacting spin-orbit-coupled Fermi gas.

cond-mat.quant-gasCross-listedarXiv:2610.38512Oct 29, 20260 citations

T

is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization

P

and the contact

C

for both repulsive and attractive Fermi gases. Our findings emphasize the role of pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.