Temperature and doping induced instabilities of the repulsive Hubbard model on Lieb lattice

TL;DR

This study investigates how temperature and doping influence the phases of the repulsive Hubbard model on the Lieb lattice, revealing non-Fermi liquid behavior, magnetic order, Mott insulators, and stripe phases driven by flat band effects.

Contribution

It provides a detailed analysis of finite-temperature and doping effects on the Hubbard model on the Lieb lattice, highlighting flat band induced phenomena using real-space DMFT and quantum Monte Carlo methods.

Findings

Identification of non-Fermi liquid behavior linked to flat band singularity.

Discovery of a magnetically ordered phase with linear order parameter dependence.

Observation of stripe order and sub-lattice ordering away from half-filling.

Abstract

The properties of a phase at finite interactions can be significantly influenced by the underlying dispersion of the non-interacting Hamiltonian. We demonstrate this by studying the repulsive Hubbard model on the $2$D Lieb lattice, which has a flat band for vanishing interaction $U$. We perform real-space dynamical mean-field theory calculations at different temperatures and dopings using a continuous time quantum Monte Carlo impurity solver. Studying the frequency dependence of the self-energy, we show that a finite temperature non-magnetic non-Fermi liquid behavior is a concomitant of the flat band singularity. At half-filling we also find a magnetically ordered region, where the order parameter varies linearly with the interaction strength, and a strongly correlated Mott insulating phase. The double occupancy decreases sharply for small $U$, highlighting the flat band contribution. Away from half-filling, we observe the stripe order, i.e. an inhomogeneous spin and charge density wave of finite wavelength which turns into a sub-lattice ordering at higher temperatures.