Phase diagrams of one-dimensional half-filled two-orbitalSU(N)cold fermion systems

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 twoorbital 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 (nondegenerate, 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 nonlocal order parameters that characterize the SU(N ) topological phases found here.

Interaction-induced exotic vortex states in an optical lattice clock with spin-orbit coupling

“…While the SDW order mainly decreases the energy of the attractive inter-orbital spin-preserving interactions. These are consistent with previous studies on the SU(2) ladder systems [41,43]. Note that for the phase diagrams in Figs.…”

“…Here, |↑ and |↓ label different spin states in the |g or |e hyperfine manifolds. As reported in previous studies, such an inter-orbital spin-exchange interaction would induce density-ordered states in either the spin or the charge channel, leading to spin-density wave (SDW), orbital-density order (ODW) or charge-density wave (CDW) phases [40][41][42][43][44][45][46][47][48]. More interestingly, these interactions would couple the otherwise independent ladders, which may induce new patterns of current flow in the system.…”

One-dimensional two-orbital SU(N) ultracold fermionic quantum gases at incommensurate filling: A low-energy approach

“…We first consider the isotropic case with t g = t e and U gg = U ee so that the oneloop RG equations are still given by Eqs. (24) with the initial conditions (14). The numerical analysis is presented in Fig.…”

“…In this respect, several two-orbital SU(N ) fermionic lattice models with contact interactions can be considered in the context of alkalineearth-like atoms. 2,14,16,32,33 A first lattice model, the g − e model, which is directly relevant to recent experiments, [26][27][28] is defined from the existence of four different scattering lengths that stem from the two-body collisions with g and e atomic states:…”

“…[5][6][7] It paves the way of the quantum simulation of SU(N ) manybody physics with the realization of exotic phases such as SU(N ) chiral spin liquid states or SU(N ) symmetry-protected topological phases. [8][9][10][11][12][13][14][15][16][17][18] A second important property of alkaline-earth-like atoms is the existence of a long-lived metastable excited state ( 3 P 0 ) coupled to the ground state ( 1 S 0 ) via an ultranarrow doublyforbidden transition. This makes them ideal systems for the realization of the most precise atomic clocks.…”