The ground state, localization, and chiral edge dynamics of a three-legged bosonic magnetic ladder

Abstract

Three-legged bosonic/fermionic magnetic ladder, reproducing the main features of magnetic lattice systems, is an ideal model to study the edge-bulk coupling and chiral edge dynamics, which are a hallmark of quantum Hall physics. Here, the ground state transition, localization, and chiral edge (bulk) states of an interacting three-legged bosonic magnetic ladder are studied analytically and numerically. When the system is in a quasi-steady state, using variational analysis, the threshold for the transition from zero momentum state to plane wave state is obtained. The energy spectrum, the ground state diagram, the chiral current of the system are presented, and the chiral current reversal at the state transition point is observed. Furthermore, the localization and its stability in the system are discussed, and rich localized phenomena (diffusion, breather, soliton, and self-trapping) are predicted. Stable soliton/breather prefers to form an edge state, while the self-trapping is favorite to form a bulk state, i.e. localized edge and bulk states are obtained. Particularly, for the unstable soliton in the ground state or metastable state, different kinds of chiral edge/bulk state and edge-bulk coupling are observed. The stability of the localized states, the edge-bulk coupling characteristics, and the chirality of the system depend on the energy band structure of the system. Additionally, a controllable transition between localized edge state and bulk state is realized by quenching the soliton state. We proposed a theoretical evidence to design and manipulate edge-bulk coupling and different kinds of localized/chiral edge (bulk) states in three-legged bosonic magnetic ladder.