Lee-Yang zeroes in the one flavour massive lattice Schwinger model

TL;DR

This paper investigates the phase structure of the one-flavor lattice Schwinger model using analytical and numerical methods, focusing on Lee-Yang zeroes to identify phase transition lines across different coupling regimes.

Contribution

It provides an analytical solution for the partition function at strong coupling and explores Lee-Yang zeroes to map phase transitions in the model.

Findings

Support for a phase transition line from weak to strong coupling.

Analytical solution for the partition function up to 8x8 lattice.

Identification of critical hopping parameter values at different couplings.

Abstract

We study the partition function of the model formulated with Wilson fermions with only one species, both analytically and numerically. At strong coupling we construct the solution for lattice size up to $8\times 8$, a polynomial in the hopping parameter up to $O(\ka^{128})$. At $\be>0$ we evaluate the expectation value of the fermion determinant for complex values of $\ka$. From the Lee-Yang zeroes we find support for the existence of a line of phase transitions from $(\be=0, \ka\simeq 0.38)$ up to $(\be=\infty, \ka=1/4)$.