We study an interacting two-component hard-core bosons on square lattice for which, in the presence of staggered magnetic flux, the ground state is a bosonic integer quantum Hall (BIQH) state. Using a coupled-wire bosonization approach, we analytically show this model exhibits a BIQH state at total charge half filling associated with a symmetry-protected topological phase under U(1) charge conservation. These theoretical expectations are verified, using the infinite density matrix renormalization group method, by providing numerical evidences for: (i) a quantized Hall conductance σ_xy=±2, and (ii) two counter-propagating gapless edge modes. Our model is a bosonic cousin of the fermionic Haldane model and serves as an additional case of analogy between bosonic and fermionic quantum Hall states.

We study the phase diagram of the interacting fermionic two-leg ladder, which is featured by pair hopping and interactions of singlet and triplet superconducting channels. By using Abelian bosonization method, we obtain the full phase diagram of our model. The superconducting triplet pairing phase is characterized by a fractional edge spin and interpreted as two Kitaev chains under the mean filed approximation. The pair hopping will give rise to spin-density-wave（SDW）orders and can also support Majorana edge modes in spin channel. At half filling, the resulting Majorana-SDW phase shows additional fractionalization in charge channel, and can be interpreted as two Su–Schrieffer–Heeger（SSH） chains in the mean field regime.

One promising avenue to study one-dimensional (1D) topological phases is to realize them in synthetic materials such as cold atomic gases. Intriguingly, it is possible to realize Majorana boundary modes in a 1D number-conserving system consisting of two fermionic chains coupled only by pair-hopping processes [C. V. Kraus et al., Phys. Rev. Lett. 111, 173004 (2013)]. It is commonly believed that significant interchain single-particle tunneling necessarily destroys these Majorana modes, as it spoils the Z(2) fermion-parity symmetry that protects them. In this Rapid Communication, we present a mechanism to overcome this obstacle, by piercing a (synthetic) magnetic pi flux through each plaquette of the Fermi ladder. Using bosonization, we show that in this case there exists an exact leg-interchange symmetry that is robust to interchain hopping, and acts as fermion parity at long wavelengths. We utilize density matrix renormalization group and exact diagonalization to verify that the resulting model exhibits Majorana boundary modes up to large single-particle tunnelings, comparable to the intrachain hopping strength. Our work highlights the unusual impacts of different topologically trivial band structures on these interaction-driven topological phases, and identifies a distinct route to stabilizing Majorana boundary modes in 1D fermionic ladders.

We study the orbital effects of the synthetic magnetic fields in an interacting square lattice two-leg fermionic ladder model with the number-conserving pair hopping that hosting the Majorana bound states. By utilizing density matrix renormalization group and exact diagonalization, we identify a novel type-II topological Meissner (topo-Meissner) phase (as distinguished from the low-field type-I topo-Meissner state) when threading a high magnetic flux through the plaquette of the ladder, which not only exhibits a large uniformly circulating chiral current along the legs, the characteristics of the celebrated Meissner state, but also accommodates a topologically protected ground-state manifold due to the reentrant emergence of the Majorana end modes. Our work reveals some interesting interference effects resulting from the interplay between the gauge fields and the strong interactions in establishing the intrinsic topological states of matter in low-dimensional quantum systems.