Branch-cut Singularities in Thermodynamics of Fermi Liquid Systems

The recently measured spin susceptibility of the two dimensional electron gas exhibits a strong dependence on temperature, which is incompatible with the standard Fermi liquid phenomenology. Here we show that the observed temperature behavior is inherent to ballistic two dimensional electrons. Besides the single-particle and collective excitations, the thermodynamics of Fermi liquid systems includes effects of the branch-cut singularities originating from the edges of the continuum of pairs of quasiparticles. As a result of the rescattering induced by interactions, the branch-cut singularities generate non-analyticities in the thermodynamic potential which reveal themselves in anomalous temperature dependences. Calculation of the spin susceptibility in such a situation requires a non-perturbative treatment of the interactions. As in high-energy physics, a mixture of the collective excitations and pairs of quasiparticles can be effectively described by a pole in the complex momentum plane. This analysis provides a natural explanation for the observed temperature dependence of the spin susceptibility, both in sign and magnitude.