Exact diagonalization study of the trionic crossover and the trion liquid in the attractive three-component Hubbard model

TL;DR

This study uses exact diagonalization to explore the formation of trions and their properties in an attractive three-component Hubbard model, revealing a smooth crossover to a trionic regime with distinct spectral and correlation features.

Contribution

It provides a detailed analysis of the trionic crossover and effective trionic liquid in the three-component Hubbard model using exact diagonalization, highlighting spectral gaps and correlation changes.

Findings

Clear gap opening at U_c ~ 1.8t indicating trion formation

Power-law to exponential decay transition in pairing correlations

Effective trionic liquid modeled as spinless heavy fermions with strong repulsion

Abstract

We investigate the trion formation and the effective trionic properties in the attractive Hubbard model with three fermionic colors using exact diagonalization. The crossover to the trionic regime with colorless compound fermions upon increasing strength of the onsite attraction parameter U features smoothly evolving ground state properties and exhibits clear similarities to the BCS/BEC-crossover for two colors. In the excitation spectrum, there is a clear gap opening between a band of well-defined trions and excitations of broken-up trions at U_c ~ 1.8t. This picture remains the same away from the SU(3)-symmetric point. The spatial pairing correlations for colored Cooper pairs are compatible with a power-law at small attractions and change to an exponential decay above the trionic crossover. Furthermore, we show that the effective trionic liquid for U > U_c can be well modeled with spinless 'heavy' fermions interacting with a strong nearest neighbor repulsion.