Topological phases protected by projective PT symmetry in alkaline-earth-like atoms

Sylvain Capponi, Heloise Nonne, Marion Moliner +2 more

De-Huan Cai, Wei Yi

Sheng-Jie Huang, Hao Song, Michael Hermele

Heloise Nonne, Marion Moliner, Sylvain Capponi +2 more

We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at halffilling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p -band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2 I + 1) symmetry which depend only on the nuclear-spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I (=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2 I + 1) symmetry.

Xiaofan Zhou, Suotang Jia, Jian-Song Pan

An important aspect in categorizing topological phases is whether the system is spinless or spinful, given that these classes exhibit distinct symmetry algebras, leading to disparate topological classifications. By utilizing the projective presentation strategy, the topological phases of spinless (or spinful) systems can be emulated using spinful (or spinless) systems augmented with gauge fields. In this study, we propose to implement the topological phases safeguarded by the unique projective space-time inversion symmetry inherent to spinful models, using synthetic spinless alkaline-earth-metal-like atoms. Employing the separation of orbital and nuclear-spin degrees of freedom, the model is configured as a rectangular tube penetrated by a uniform magnetic flux through each plaquette, which simulates a spinless ladder endowed with projective space-time inversion symmetry satisfying the algebraic properties of a spinful model. For interacting topological phases with interorbital spin-exchange interactions, which also adhere to space-time inversion symmetry, the four-fold degeneracy of edge modes is split into two pairs of edge modes with two-fold degeneracy. We map the complete phase diagram in the end and discover that these interacting topological phases ultimately evolve into distinct charge-density-wave phases via spontaneous symmetry breaking.

Bei Zeng, Xie Chen, D. L. Zhou +1 more