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

We investigate the zero-temperature phase diagram of two-orbital SU(N) fermionic models at incommensurate filling which are directly relevant to strontium and ytterbium ultracold atoms loading into a one-dimensional optical lattice. Using a low-energy approach that takes into account explicitly the SU(N) symmetry, we find that a spectral gap for the nuclear-spin degrees of freedom is formed for generic interactions. Several phases with one or two gapless modes are then stabilized which describe the competition between different density instabilities. In stark contrast to the N=2 case, no dominant pairing instabilities emerge and the leading superfluid one is rather formed from bound states of 2N fermions.Comment: 11 pages, 4 figure

Haldane phases with ultracold fermionic atoms in double-well optical lattices

International audienceWe propose to realize one-dimensional topological phases protected by SU(N) symmetry using alkali or alkaline-earth atoms loaded into a bichromatic optical lattice. We derive a realistic model for this system and investigate it theoretically. Depending on the parity of N, two different classes of symmetry-protected topological (SPT) phases are stabilized at half-filling for physical parameters of the model. For even N, the celebrated spin-1 Haldane phase and its generalization to SU(N) are obtained with no local symmetry breaking. In stark contrast, at least for N=3, a new class of SPT phases, dubbed chiral Haldane phases, that spontaneously break inversion symmetry, emerges with a twofold ground-state degeneracy. The latter ground states with open-boundary conditions are characterized by different left and right boundary spins, which are related by conjugation. Our results show that topological phases are within close reach of the latest experiments on cold fermions in optical lattices

Entanglement topological invariants for one-dimensional topological superconductors

Entanglement provides characterizing features of true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground-state manifold and are thus quantized to 0 or log2. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and nontrivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques

Symmetry-protected topological phases in two-leg SU(N) spin ladder with unequal spins

Chiral Haldane phases are examples of one-dimensional topological states of matter which are protected by projective SU($N$) group (or its subgroup $\mathbb{Z}_N \times \mathbb{Z}_N$) with $N>2$. The unique feature of these symmetry protected topological (SPT) phases is that they are accompanied by inversion-symmetry breaking and the emergence of different left and right edge states which transform, for instance, respectively in the fundamental ($\boldsymbol{N}$) and anti-fundamental ($\overline{\boldsymbol{N}}$) representations of SU($N$). We show, by means of complementary analytical and numerical approaches, that these chiral SPT phases as well as the non-chiral ones are realized as the ground states of a generalized two-leg SU($N$) spin ladder in which the spins in the first chain transform in $\boldsymbol{N}$ and the second in $\overline{\boldsymbol{N}}$. In particular, we map out the phase diagram for $N=3$ and $4$ to show that {\em all} the possible symmetry-protected topological phases with projective SU($N$)-symmetry appear in this simple ladder model

Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

We study the disconnected entanglement entropy, S-D, of the Su-Schrieffer-Heeger model. S-D is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that S-D behaves like a topological invariant, i.e., it is quantized to either 0 or 2 log(2) in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, S-D displays a finitesize scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of S-D, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants associated with particle-hole symmetry. (C) Copyright T. Micallo et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation