Symmetry protected topological phases in two-orbital SU(4) fermionic atoms

TL;DR

This paper investigates a one-dimensional SU(4) fermionic system, revealing a novel symmetry protected topological phase with sixfold edge degeneracy, distinct from known SU(4) SPT phases, using numerical and matrix product state methods.

Contribution

It identifies a new SU(4) SPT phase with topological index 2 and six edge states, expanding understanding of topological phases in multi-orbital fermionic systems.

Findings

Ground state is a nontrivial SPT phase with $Z_4 \times Z_4$ symmetry.

The SPT phase has a topological index of 2 in $\mathbb{Z}_4$.

Sixfold degenerate edge states are observed in the SPT phase.

Abstract

We study one-dimensional systems of two-orbital SU(4) fermionic cold atoms. In particular, we focus on an SU(4) spin model [named SU(4) $e$-$g$ spin model] that is realized in a low-energy state in the Mott insulator phase at the filling $n_g=3, n_e=1$ ($n_g, n_e$: numbers of atoms in ground and excited states, respectively). Our numerical study with the infinite-size density matrix renormalization group shows that the ground state of SU(4) $e$-$g$ spin model is a nontrivial symmetry protected topological (SPT) phase protected by $Z_4 \times Z_4$ symmetry. Specifically, we find that the ground state belongs to an SPT phase with the topological index $2\in\mathbb{Z}_4$ and show sixfold degenerate edge states. This is topologically distinct from SPT phases with the index $1\in\mathbb{Z}_4$ that are realized in the SU(4) bilinear model and the SU(4) Affleck-Kennedy-Lieb-Tasaki (AKLT) model. We explore the phase diagram of SU(4) spin models including $e$-$g$ spin model, bilinear-biquadratic model, and AKLT model, and identify that antisymmetrization effect in neighboring spins (that we quantify with Casimir operators) is the driving force of the phase transitions. Furthermore, we demonstrate by using the matrix product state how the $\mathbb{Z}_4$ SPT state with six edge states appears in the SU(4) $e$-$g$ spin model.