Partition function zeros of quantum many-body systems

Abstract

We present a new method for calculating the Yang-Lee partition function zeros of a translationally invariant model of lattice fermions, exemplified by the Hubbard model. The method rests on a theorem involving the single electron self-energy $\hat{I}{\pounds }_{\ddot{I}}ƒ(k,i\ddot{I}{‰}_n)$ in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wavevector and spin labeled virtual energies $\hat{I}{¾}_{k\ddot{I}ƒ}$. These, thermodynamically derived virtual energies, are solutions of equations involving the self-energy at corresponding $k\ddot{I}ƒ$'s. Examples of the method in simplified situations are provided.

32 pages, 4 figures