Ultra-soft fermionic excitation at finite chemical potential

Abstract

It has been suggested previously that an ultra-soft fermionic excitation develops, albeit with a small spectral weight, in a system of massless fermions and scalar bosons with Yukawa interaction at high temperature ($T$). In this paper we study how this excitation is modified at finite chemical potential ($μ$). We relate the existence of the ultra-soft mode to symmetries, in particular charge conjugation, and a supersymmetry of the free system which is spontaneously broken by finite temperature and finite density effects, as argued earlier by Lebedev and Smilga. A non vanishing chemical potential breaks both symmetries explicitly, and maximally at zero temperature where the mode ceases to exist. A detailed calculation indicates that the ultra-soft excitation persists as long as $T\gtrsim μ$.

10 pages, 8 figures. v2: Figs. 7 and 8 are added, detailed discussion on value of chemical potential in which the ultrasoft mode persists are added in Sec. III-C