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 ${\Sigma }_{\sigma }(k,i{\omega }_n)$ in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wavevector and spin labeled virtual energies ${\xi }_{k\sigma }$. These, thermodynamically derived virtual energies, are solutions of equations involving the self-energy at corresponding $k\sigma$'s. Examples of the method in simplified situations are provided.

32 pages, 4 figures

References in corpus (8)

• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Imaginary chemical potential and finite fermion density on the lattice
• Observation of Lee-Yang zeros
• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
• Lee-Yang theory of criticality in interacting quantum many-body systems
• Exact Fisher zeros and thermofield dynamics across a quantum critical point
• DiracQ: A Quantum Many-Body Physics Package

Cited by in corpus (1)

• Lee-Yang-zero ratio method in three-dimensional Ising model