Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems

TL;DR

This paper explores the phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermion systems, revealing various Mott-insulating and topological phases, including novel SU(N) SPT phases, using analytical and numerical methods.

Contribution

It provides the first detailed phase diagram of two-orbital SU(N) fermionic systems, identifying new topological phases and characterizing them with entanglement and non-local order parameters.

Findings

Identification of orbital-Haldane and SU(N) topological phases

Mapping of zero-temperature phase diagrams at half-filling

Proposal of non-local order parameters for topological phases

Abstract

We investigate possible realizations of exotic SU(N) symmetry-protected topological (SPT) phases with alkaline-earth cold fermionic atoms loaded into one-dimensional optical lattices. A thorough study of two-orbital generalizations of the standard SU(N) Fermi-Hubbard model, directly relevant to recent experiments, is performed. Using state-of-the-art analytical and numerical techniques, we map out the zero-temperature phase diagrams at half-filling and identify several Mott-insulating phases. While some of them are rather conventional (non-degenerate, charge-density-wave or spin-Peierls like), we also identify, for even-N, two distinct types of SPT phases: an orbital-Haldane phase, analogous to a spin-N/2 Haldane phase, and a topological SU(N) phase, which we fully characterize by its entanglement properties. We also propose sets of non-local order parameters that characterize the SU(N) topological phases found here.