An Unconventional Deformation of the Spin-1/2 Fermi Gas*

Interacting bosonic and fermionic systems can be expressed in terms of their noninteracting versions (in an external field) by using a Hubbard-Stratonovich transformation. When treating interactions in that fashion, the quantum statistics enters through the form of the noninteracting partition functions $mathcal{Z}_0$. The logarithm of $mathcal{Z}_0$ for bosons and fermions are distinguished mathematically, by the former being given by an infinite series, while the latter is a truncated sum due to the Pauli principle. By truncating the bosonic series in different ways, one obtains an extension of quantum statistics in an unconventional direction that interpolates between fermions and bosons, where only up to K particles may occupy a single-particle state, with K varying between 1 and infinity.

In this work, we explore such a deformation in a particular case, which amounts to twisting the chemical potential of the Fermi gas in the complex plane.  In particular, in the conformally invariant case of the unitary limit of spin-1/2 fermions, we obtain a class of equally conformally invariant theories of particles obeying alternate statistics. We provide a first description of the thermodynamics of such a system and compare it with known results for conventional spin-1/2 fermions.