Interacting Fermions in One Dimension. I. Repulsive Potential

We explore a few-fermion mixture consisting of two components which are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermisea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multi-configurational time-dependent Hartree (MCTDH) method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our Ansatz for a correlated pair wave-function proposed in [1] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single impurity atom shows rich behaviour of the energy and density as we approach fermionization, and is directly connected to recent experiments [2][3][4].

Section: Introductionmentioning

confidence: 99%

Two-component few-fermion mixtures in a one-dimensional trap: Numerical versus analytical approach

Brouzos

Schmelcher

2013

“…On the other hand, one might be able to gain important insights by studying the counterpart problem in 1D, where the exact solutions can be accessible [21] and effective spin-chain models can be established in strong coupling limit [22][23][24][25][26][27][28]. For 1D fermion system, the ferromagnetic transition has been exactly proved with arbitrary number and arbitrary potential [29], and the polaron problem in continuum has also been exactly solved by McGuire in 1960's [30,31] and recently by Guan [32]. In particular, a negative effective mass (m * < 0) has been demonstrated for the excited upper branch of 1D Fermi polarons with attractive coupling [31], i.e., in the fermionic super Tonks-Girardeau regime [33,34].…”

Section: Introductionmentioning

confidence: 99%

“…[30,31], to study its ground state and low-lying excitation properties, including the total spin, quasi-momentum distribution and pair correlations. We find that the excited states always have the same total spin as the ground state regardless of the sign of m * , and there is no ferromagnetic component.…”

Section: Introductionmentioning

confidence: 99%

Repulsive Fermi polarons with negative effective mass

Cui

2017

Recent LENS experiment on a 3D Fermi gas has reported a negative effective mass (m * < 0) of Fermi polarons in the strongly repulsive regime. There naturally arise a question whether the negative m * is a precursor of the instability towards phase separation (or itinerant ferromagnetism). In this work, we make use of the exact solutions to study the ground state and excitation properties of repulsive Fermi polarons in 1D, which can also exhibit a negative m * in the super Tonks-Girardeau regime. By analyzing the total spin, quasi-momentum distribution and pair correlations, we conclude that the negative m * is irrelevant to the instability towards ferromagnetism or phase separation, but rather an intrinsic feature of collective excitations for fermions in the strongly repulsive regime. Surprisingly, for large and negative m * , such excitation is accompanied with a spin density modulation when the majority fermions move closer to the impurity rather than being repelled far away, contrary to the picture of phase separation. These results shed light on the recent observation of negative m * in the 3D repulsive Fermi polarons.

“…The study of multicomponent integrable systems really begins with the spin-1/2 fermion problem [24][25][26][27][28]. An interesting feature of this system is that the attractive case has a correspondence to a bosonic system with twice the interaction, in the sense that the equation for the ground state and particle energy coincide up to a sign [28].…”

Section: Introductionmentioning

confidence: 99%

Equilibrium thermodynamic properties of interacting two-component bosons in one dimension

Klauser

Caux

2011

Equilibrium thermodynamic properties of interacting two-component bosons in one dimensionKlauser, A.M.; Caux, J.S. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Download date: 12 May 2018PHYSICAL REVIEW A 84, 033604 (2011) The interplay of quantum statistics, interactions, and temperature is studied within the framework of the bosonic two-component theory with repulsive delta-function interaction in one dimension. We numerically solve the thermodynamic Bethe ansatz and obtain the equation of state as a function of temperature and of the interaction strength, the relative chemical potential, and either the total chemical potential or a fixed number of particles, allowing quantification of the full crossover behavior of the system between its low-temperature ferromagnetic and high-temperature unpolarized regime, and from the low coupling decoherent regime to the fermionization regime at high interaction. Equilibrium thermodynamic properties of interacting two-component bosons in one dimension