Monte Carlo study of fermionic trions in a square lattice with harmonic confinement

TL;DR

This paper explores the behavior of three-component fermionic trions in an optical lattice under strong attraction, revealing their spatial arrangements and density wave formations through Monte Carlo simulations, with implications for understanding correlated quantum phases.

Contribution

It derives an effective Hamiltonian for fermionic trions and demonstrates their spatial ordering and density wave phenomena in a confined lattice environment.

Findings

Trions form antiferromagnetic Ising-like states.

Density waves and coexistence of phases depend on confinement and temperature.

Proximity effects induce density modulations beyond local density approximation.

Abstract

We investigate the strong-coupling limit of a three-component Fermi mixture in an optical lattice with attractive interactions. In this limit bound states (trions) of the three components are formed. We derive an effective Hamiltonian for these composite fermions and show that it is asymptotically equivalent to an antiferromagnetic Ising model. By using Monte-Carlo simulations, we investigate the spatial arrangement of the trions and the formation of a trionic density wave (CDW), both in a homogeneous lattice and in the presence of an additional harmonic confinement. Depending on the strength of the confinement and on the temperature, we found several scenarios for the trionic distribution, including coexistence of disordered trions with CDW and band insulator phases. Our results show that, due to a proximity effect, staggered density modulations are induced in regions of the trap where they would not otherwise be present according to the local density approximation.