Partition function zeros of quantum many-body systems.

Abstract

We present a 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 usual single-electron self-energy Σ_{σ}(k[over ⃗],iω_{n}|μ) with chemical potential μ, in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wave vector and spin labeled virtual energies ξ_{k[over ⃗]σ}. These, thermodynamically derived virtual energies, are solutions of the set of equations ξ_{kσ}=ɛ_{σ}(k[over ⃗])-1/2U+Σ_{σ}(k[over ⃗],iπ/β|ξ_{kσ}+1/2U-iπ/β)=0. Examples of the method in simplified situations are provided.