Phases of one-dimensional SU(N) cold atomic Fermi gases --from molecular Luttinger liquids to topological phases

TL;DR

This paper reviews the diverse phases of one-dimensional SU(N) cold atomic Fermi gases, highlighting novel phenomena such as molecular Luttinger liquids and topological phases, with a focus on models with additional orbital degrees of freedom.

Contribution

It introduces new microscopic models for SU(N) fermionic systems with orbital degrees of freedom and discusses their rich phase diagrams, including topological phases.

Findings

Rich phase diagram for N>2 including Luttinger liquids and Mott insulators

Presence of symmetry-protected topological phases with edge states

Enhanced exotic phenomena compared to SU(2) systems

Abstract

Alkaline-earth and ytterbium cold atomic gases make it possible to simulate SU(N)-symmetric fermionic systems in a very controlled fashion. Such a high symmetry is expected to give rise to a variety of novel phenomena ranging from molecular Luttinger liquids to (symmetry- protected) topological phases. We review some of the phases that can be stabilized in a one dimensional lattice. The physics of this multicomponent Fermi gas turns out to be much richer and more exotic than in the standard SU(2) case. For N > 2, the phase diagram is quite rich already in the case of the single-band model, including a molecular Luttinger liquid (with dominant superfluid instability in the N-particle channel) for incommensurate fillings, as well as various Mott-insulating phases occurring at commensurate fillings. Particular attention will be paid to the cases with additional orbital degree of freedom (which is accessible experimentally either by taking into account two atomic states or by putting atoms in the p-band levels). We introduce two microscopic models which are relevant for these cases and discuss their symmetries and strong coupling limits. More intriguing phase diagrams are then presented including, for instance, symmetry protected topological phases characterized by non-trivial edge states.