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 ${\mathrm{\Sigma }}_{\sigma }(\vec{k},i{\omega }_n|\mu )$ with chemical potential $\mu$, in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wave vector and spin labeled virtual energies ${\xi }_{\vec{k}\sigma }$. These, thermodynamically derived virtual energies, are solutions of the set of equations ${\xi }_{k\sigma }={\varepsilon }_{\sigma }\left(\vec{k}\right)-\frac{1}{2}U+{\mathrm{\Sigma }}_{\sigma }(\vec{k},i\frac{\pi }{\beta }|{\xi }_{k\sigma }+\frac{1}{2}U-i\frac{\pi }{\beta })=0$. Examples of the method in simplified situations are provided.

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• Equations of state
• Quantum statistical mechanics