Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice

TL;DR

This paper investigates how electronic correlations induce spontaneous charge order and particle-hole symmetry breaking in spinless fermions on the Lieb lattice, revealing a finite-temperature transition and a new route to doping without a sign problem.

Contribution

It demonstrates the spontaneous breaking of particle-hole symmetry and charge order in the $t$-$V$ model on the Lieb lattice using advanced Monte Carlo simulations, offering insights into correlated fermion behavior.

Findings

Finite-temperature Ising transition to charge density wave

Spontaneous particle-hole symmetry breaking

Charge order with one electron and two holes per unit cell

Abstract

We study spinless fermions with nearest-neighbor repulsive interactions ($t$-$V$ model) on the two-dimensional three-band Lieb lattice. At half-filling, the free electronic band structure consists of a flat band at zero energy and a single cone with linear dispersion. The flat band is expected to be unstable upon inclusion of electronic correlations, and a natural channel is charge order. However, due to the three-orbital unit cell, commensurate charge order implies an imbalance of electron and hole densities and therefore doping away from half-filling. Our numerical results show that below a finite-temperature Ising transition a charge density wave with one electron and two holes per unit cell and its partner under particle-hole transformation are spontaneously generated. Our calculations are based on recent advances in auxiliary-field and continuous-time quantum Monte Carlo simulations that allow sign-free simulations of spinless fermions at half-filling. It is argued that particle-hole symmetry breaking provides a route to access levels of finite doping, without introducing a sign problem.