Theory of bound states of fermions in many-body systems

José M. Arias, María Isabel Gallardo, Manuel Lozano

Daniel Charles Mattis, Sergey Rudin

The theory of three-body bound states for particles moving on a lattice and interacting with attractive two-body pointlike potentials is presented. The applications are to bosons, fermions (no three-body bound states are found), and magnons. When a three-body bound state forms in three dimensions, it does so discontinuously. Thus there is a maximum size for the three-body bound state, of approximately two lattice constants. Some of the various analyses are relevant to magnetism and superconductivity.

Theoretical Physics

Gerhard Bräunlich, Christian Hainzl, Robert Seiringer

We consider the Bogolubov–Hartree–Fock functional for a fermionic many-body system with two-body interactions. For suitable interaction potentials that have a strong enough attractive tail in order to allow for two-body bound states, but are otherwise sufficiently repulsive to guarantee stability of the system, we show that in the low-density limit the ground state of this model consists of a Bose–Einstein condensate of fermion pairs. The latter can be described by means of the Gross–Pitaevskii energy functional.

Pierre Gaspard, Sudhir R Jain

Martin Schäfer, Lorenzo Contessi, Johannes Kirscher +1 more

We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into clusters, if mixed-symmetry of its wave function is enforced. We claim that any theory in which the two-body scattering length is much larger than any other scale involved exhibits such instability. We exemplify this with the inability of the leading-order pionless effective field theory to describe stable states of A>4 nuclei. A finite interaction range is identified as a sufficient condition for a bound mixed-symmetry system. The minimal value of this range depends on the proximity of a system to unitarity, on the number of constituents, and on the particular realization of discrete scale invariance of the three-body spectrum.