Effective theory for strongly attractive one-dimensional fermions
arXiv:2412.05915 · doi:10.1103/8mnc-x42q
Abstract
We study a one-dimensional system of two-component fermions in the limit of strong attractive particle-particle interactions. First, we analyze scattering in the corresponding few-body problem, which is analytically solvable via Bethe ansatz. This allows us to engineer effective interactions between the system's effective degrees of freedom: fermions and bosonic dimers (tightly bound pairs of fermions). We argue that, although these interactions are strong, the resulting effective problem can be mapped onto a weakly interacting one, paving the way for the use of perturbation theory. This finding simplifies studies of many-fermion systems under confinement that are beyond reach of state-of-the-art numerical methods. We illustrate this statement by considering an impurity atom in a Fermi gas.
Version accepted for publication in Physical Review Letters
References in corpus (37)
- Energetics of a strongly correlated Fermi gas
- Fermi gases in one dimension: From Bethe Ansatz to experiments
- A one-dimensional liquid of fermions with tunable spin
- From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
- Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
- An exactly solvable model of the BCS-BEC crossover
- Tan relations in one dimension
- Tuning the interactions of spin-polarized fermions using quasi-one-dimensional confinement
- One-dimensional mixtures of several ultracold atoms: a review
- Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
- Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
- Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
- Fermionization of two-component few-fermion systems in a one-dimensional harmonic trap
- Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
- Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions
- Interacting fermions in quasi-one-dimensional harmonic traps
- Causality and the effective range expansion
- Theory of spinor Fermi and Bose gases in tight atom waveguides
- Trapped one-dimensional ideal Fermi gas with a single impurity
- Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
- Analytic Harmonic Approach to the N-body problem
- Two-flavor mixture of a few fermions of different mass in a one-dimensional harmonic trap
- Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement
- One-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branch
- Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas
- Strongly interacting trapped one-dimensional quantum gases: an exact solution
- Quantum scattering in one dimension
- Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
- Three interacting atoms in a one-dimensional trap: A benchmark system for computational approaches
- Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
- Diffractive scattering of three particles in one dimension: a simple result for weak violations of the Yang--Baxter equation
- Multicomponent Strongly Interacting Few-Fermion Systems in One Dimension
- Magnetic impurity in a one-dimensional few-fermion system
- Eliminating the wave function singularity for ultracold atoms by similarity transformation
- Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions
- Binding of heavy fermions by a single light atom in one dimension
- Morphology of three-body quantum states from machine learning