Ground State Phase Diagram of $\text{SU}(3)$ $t$-$J$ Chain

TL;DR

This study maps the ground state phases of the $ ext{SU}(3)$ $t$-$J$ chain, revealing a rich phase diagram with Luttinger liquid, spin-gapped Luther-Emery liquid, and phase separation, and uncovers molecular superfluid order.

Contribution

It provides the first detailed phase diagram of the $ ext{SU}(3)$ $t$-$J$ chain using DMRG, identifying novel phases and mechanisms of molecular superfluidity.

Findings

Identification of three distinct phases: Luttinger liquid, Luther-Emery liquid, and phase separation.

Discovery of molecular superfluid quasi-long-range order in the Luther-Emery phase.

Quantitative characterization of phases through spin gap, compressibility, and correlation functions.

Abstract

Distinct from the $\text{SU}(2)$ case, the fermionic systems with $\text{SU}(N)$ symmetry are expected to exhibit novel physics, such as exotic singlet formation. Using the density matrix renormalization group technique, we obtain the ground state phase diagram of the $\text{SU}(3)$ $t$-$J$ chain for density $n<1$. The ground state phase diagram includes the Luttinger liquid, the extended Luther-Emery liquid characterized by a spin gap, and the phase separation state. We quantitatively assess the characteristics of the three phases by measuring spin gap, compressibility, various correlation functions and structure factors. We further study the extended Luther-Emery liquid phase and discover molecular superfluid quasi-long-range order. The mechanism of the molecular superfluid is the combination of three $\text{SU}(3)$ fermions on sites that are not completely connected. Accordingly, we can speculate the behavior of the $\text{SU}(N)$ $t$-$J$ chain model with larger $N$ values, operating within the same filling regime.