Edge-Edge Correlations without Edge-States: $\eta$-clustering State as Ground State of the Extended Attractive SU(3) Hubbard Chain

TL;DR

This paper investigates the phase diagram of an extended attractive SU(3) Hubbard chain, identifying phases like phase separation, TLL, and CDW, and reveals the $ ext{eta}$-clustering state as the ground state at phase boundaries, exhibiting boundary correlations.

Contribution

It introduces the $ ext{eta}$-clustering state as a ground state in the SU(3) Hubbard chain and demonstrates its boundary correlations using DMRG, extending understanding of edge-edge correlations without edge-states.

Findings

Identification of phase separation, TLL, and CDW phases.

The $ ext{eta}$-clustering state as the ground state at phase boundaries.

Numerical confirmation of analytical results using DMRG.

Abstract

We explore the phase diagram of the extended attractive SU($3$) Hubbard chain with two-body hopping and nearest-neighbor attraction at half-filling. In the large on-site attraction limit, we identify three different phases: phase separation (PS), Tomonaga-Luttinger liquid (TLL), and charge density wave (CDW). Our analysis reveals that the $\eta$-clustering state, a three-component generalization of the $\eta$-pairing state, becomes the ground state at the boundary between the PS and TLL phases. On an open chain, this state exhibits an edge-edge correlation, which we call boundary off-diagonal long-range order (bODLRO). Using the density matrix renormalization group (DMRG) method, we numerically study the phase diagram of the model with large but finite on-site interactions and find that the numerical results align with those obtained in the strong coupling limit.