Fermion quartets on the square lattice

TL;DR

This paper investigates a microscopic model of four spinless fermions on a square lattice, revealing a quartet bound state, a narrow quartet band, and a phase transition to delocalized fermions, with implications for electron quartetting phenomena.

Contribution

It introduces a detailed analysis of fermion quartets on a lattice, combining symmetry, variational, and exact methods to identify bound states and phase transitions.

Findings

Existence of a narrow quartet band at small hopping

First order transition to delocalized fermions at a critical hopping

Intermediate phase with extended hybrid quartets

Abstract

We study a microscopic model for four spinless fermions on the square lattice which exhibits a quartet bound state in the strong coupling regime. The four-particle quantum states are analyzed using symmetry arguments and by introducing a zoo of relevant lattice animals. These considerations, as well as variational and exact diagonalization calculations demonstrate the existence of a narrow quartet band at small hopping and a first order transition to delocalized fermions at a critical hopping parameter, in qualitative contrast to, e. g., the BCS-BEC crossover in the attractive Hubbard model. In the case of pure attraction, an intermediate phase is found, in which a more extended and presumably more mobile hybrid quartet dominates the ground state. We comment on the relevance of the spin degree of freedom and on the reasons why electron quartetting is rarely observed in real materials.