The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as readily realizable bridges between one-dimensional spin-orbit (time reversal) topological insulators and two-dimensional Chern insulators. We reveal three instances of their promising potential: i) they realize spin-orbit coupling, with the left-right leg degree of freedom playing the role of an effective spin, ii) their energy bands and eigenstates exactly reproduce the topological chiral edge modes of two-dimensional Chern insulators, and iii) they can be tailored to realize a topological phase transition from a trivial to a topological insulating phase. We propose realistic schemes to observe the chiral and topological properties of ladder systems with current optical lattice-based experiments. Our findings open a door to the exploration of the physics of the edges of Chern insulators and to the realization of spin-orbit coupling and topological superfluid phases with ultracold atomic gases.
Chiral Mott insulators in frustrated Bose-Hubbard models on ladders and two-dimensional lattices: a combined perturbative and density matrix renormalization group study
The Hofstadter model is a popular choice for theorists investigating the fractional quantum Hall effect on lattices, due to its simplicity, infinite selection of topological flat bands, and increasing applicability to real materials. In particular, fractional Chern insulators in bands with Chern number $|C|>1$ can demonstrate richer physical properties than continuum Landau level states and have recently been detected in experiments. Motivated by this, we examine the stability of fractional Chern insulators with higher Chern number in the Hofstadter model, using large-scale infinite density ma…
Topological nontrivial bands can be realized via Rydberg-dressed neutral atoms. We propose a two-dimensional hard-core boson model with a topological ground enrgy at band on a honeycomb lattice, where the particle hopping is realized via van der Waals interaction that exchanges the Rydberg states of two interacting atoms, while nonzero phases associated with hopping is created by transferring the optical phase of laser fields to the atomic pair wave function. Using exactly diagonalization and infinite density matrix renormalization group simulation, we find in the system a fractional Chern ins…
Recent advances in topological artificial systems open the door to realizing topological states in dimensions higher than the usual three-dimensional space. Here, we present a "tensor product" theory, which offers a method to construct Chern insulators with arbitrarily high dimensions and Chern numbers. Particularly, we show that the tensor product of a $d_A$D Chern insulator $\langle \mathcal{H}_A^{(κ_{A})}, C_A\rangle$ with a $d_B$D Chern insulator $\langle \mathcal{H}_B^{(κ_B)}, C_B\rangle$ leads to a $(d_A+d_B)$D Chern insulator $\langle \mathcal{H}_{A B}^{(κ_A\star κ_B)},-2C_AC_B\rangle $…
We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle en…
Ladder architectures are fruitful systems to realize topological phases of matter. Here we present a classification of ladder models giving rise to topological insulators. We identify six different types of topological ladder models, three in the BDI symmetry class, and three in the AIII symmetry class. They correspond to six distinct configurations of Wilson fermions. The six types are manifested in distinctive momentum distributions of the corresponding topological edge modes. The number of Wilson fermions, their chirality and mass, are directly manifested in the number, momentum and height …
We study precursor states of fractional topological insulators (FTIs) in interacting fermionic ladders with spin-orbit coupling. Within a microscopically motivated bosonization approach, we investigate different competing phases depending on same-spin and interspin interactions at fractional effective filling $ν=1/3$ per spin. In the spin-decoupled limit, we find that strong repulsive interactions of already moderate range may lead to a partially gapped state with two time-reversed copies of a quasi-one dimensional Laughlin phase. This FTI precursor competes with an interleg partially gapped p…
We propose to uncover the topology of a pseudo-Hermitian Chern insulator by quantum quench dynamics. The Bloch Hamiltonian of the pseudo-Hermitian Chern insulator is defined in the basis of the q-deformed Pauli matrices, which are related to the representation of the deformed algebras. We show the bulk-surface duality of the pseudo-Hermitian phases, then further build a concrete relation between the static band topology and quench dynamics, in terms of the time-averaged spin textures. The results are also generalized into a fully nonequilibrium case where the postquench evolution is governed b…
We study the effects of disorder on the topological Chern insulating phase in the Harper--Hofstadter--Hatsugai (HHH) model. The model with half flux has a bulk band gap and thus exhibits a nontrivial topological phase. We consider two typical types of disorder: on-site random disorder and the Aubry--Andre type quasi-periodic potential. Using the coupling matrix method, we clarify the global topological phase diagram in terms of the Chern number. The disorder modifies the gap closing behavior of the system. This modification induces the Chern insulating phase even in the trivial phase parameter…
