Recent advances in description of few two-component fermions

TL;DR

This paper reviews recent theoretical progress in modeling few two-component fermions, focusing on zero-range interactions, three- and four-body spectra, and the Efimov effect near a critical mass ratio.

Contribution

It provides a comprehensive overview of the latest developments in describing few-fermion systems, including new insights into bound states and spectral properties.

Findings

Emergence of three-body bound states at critical mass ratio

Identification of Efimov effect above the critical mass ratio

Analysis of energy spectrum crossover near the critical point

Abstract

Overview of the recent advances in description of the few two-component fermions is presented. The model of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass $m$ and a distinct particle of mass $m_1$: it turns out that two $L^P = 1^-$ three-body bound states emerge if mass ratio $m/m_1$ increases up to the critical value $\mu_c \approx 13.607$, above which the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, low-dimensional results, the four-body energy spectrum, crossover of the energy spectra for $m/m_1$ near $\mu_c $, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.