# Fermi-liquid ground state of interacting Dirac fermions in two dimensions

## TL;DR

This study uses large-scale quantum Monte Carlo simulations to demonstrate that the semimetallic phase of the 2D Hubbard model on a honeycomb lattice exhibits Fermi-liquid behavior, with a finite quasiparticle weight below a critical interaction.

## Contribution

It provides the first large-scale numerical evidence confirming Fermi-liquid behavior in the 2D correlated semimetallic phase of the Hubbard model.

## Key findings

- Quasiparticle weight remains finite below critical interaction.
- Green's function exhibits algebraic decay consistent with Fermi-liquid theory.
- Numerical simulations support Fermi-liquid description of 2D correlated metals.

## Abstract

An unbiased zero-temperature auxiliary-field quantum Monte Carlo method is employed to analyze the nature of the semimetallic phase of the two-dimensional Hubbard model on the honeycomb lattice at half filling. It is shown that the quasiparticle weight $Z$ of the massless Dirac fermions at the Fermi level, which characterizes the coherence of zero-energy single-particle excitations, can be evaluated in terms of the long-distance equal-time single-particle Green's function. If this quantity remains finite in the thermodynamic limit, the low-energy single-particle excitations of the correlated semimetallic phase are described by a Fermi-liquid-type single-particle Green's function. Based on the unprecedentedly large-scale numerical simulations on finite-size clusters containing more than ten thousands sites, we show that the quasiparticle weight remains finite in the semimetallic phase below a critical interaction strength. This is also supported by the long-distance algebraic behavior ($\sim r^{-2}$, where $r$ is distance) of the equal-time single-particle Green's function that is expected for the Fermi liquid. Our result thus provides a numerical confirmation of Fermi-liquid theory in two-dimensional correlated metals.