Singularity of the density of states in the two-dimensional Hubbard model from finite size scaling of Yang-Lee zeros

TL;DR

This paper uses finite size scaling of Yang-Lee zeros to reveal a second-order phase transition in the 2D Hubbard model, indicating a singular density of states and diverging susceptibility.

Contribution

It introduces a novel finite size scaling analysis of Yang-Lee zeros to identify phase transition behavior in the 2D Hubbard model.

Findings

Logarithmic scaling of zeros suggests a singular carrier density dependence.

Identifies a second-order phase transition with specific critical exponents.

Results imply a divergence in electronic susceptibility and singular density of states.

Abstract

A finite size scaling is applied to the Yang-Lee zeros of the grand canonical partition function for the 2-D Hubbard model in the complex chemical potential plane. The logarithmic scaling of the imaginary part of the zeros with the system size indicates a singular dependence of the carrier density on the chemical potential. Our analysis points to a second-order phase transition with critical exponent ${1\over \delta}={1\over 2}\pm {1\over 3}$ which leads to a divergence of the electronic susceptibility. We interprete these results as reflecting singular behaviour of the density of states in the quasiparticle spectrum.