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Many Body Theory for Quartets, Trions, and Pairs in Low Density Multi-Component Fermi-Systems ∗

Peter Schuck, Takaaki Sogo, GERD RÖPKE

Published Dec 3, 2012• 3 citations
OpenAlex

Abstract

A selfconsistent many body approach for the description of gases with quartets, trions, and pairs is presented. Applications to 3D Fermi systems at low density are discussed.

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Paired states, trions and quarteting states in one-dimensional SU (4) attractive fermions are investigated via exact Bethe ansatz calculations. In particular, quantum phase transitions are identified and calculated from the quarteting phase into normal Fermi liquid, trionic states and spin-2 paired states which belong to the universality class of linear field-dependent magnetization in the vicinity of critical points. Moreover, unified exact results for the ground-state energy, chemical potentials and complete phase diagrams for isospin S =1/2, 1, 3/2 attractive fermions with external fields are presented. Also identified are the magnetization plateaux of m z = M s /3 and m z =2 M s /3, where M s is the magnetization saturation value. The universality of finite-size corrections and collective dispersion relations provides a further test ground for low-energy effective field theory.
Finding the distinct features of the crossover from the regime of large overlapping Cooper pairs to the limit of non-overlapping pairs of fermions (Shafroth pairs) in multi-component Fermi systems remains a topical problem in a quantum many-body theory. Here this transition is studied by calculating the two-body density, spin and isospin correlation functions in dilute two-component Fermi superfluid, taking as an example an infinite system of protons and neutrons (nuclear matter). It is shown that criterion of the crossover [Phys. Rev. Lett. 95, 090402 (2005)], formulated for ultracold fermionic atomic gases and consisting in the change of the sign of the density correlation function at low momentum transfer, fails to describe correctly the density-driven BEC–BCS transition at finite isospin asymmetry or finite temperature. As an unambiguous signature of the BEC–BCS transition, one can use the presence (BCS regime) or absence (BEC regime) of the singularity in the momentum distribution of the quasiparticle density of states.