Topological and dynamical features of periodically driven spin ladders

TL;DR

This paper investigates the topological and dynamical properties of periodically driven spin ladders, revealing subharmonic magnetization dynamics linked to Majorana modes and highlighting their potential implications for higher-dimensional Floquet systems.

Contribution

It introduces the topological features of driven spin ladders, especially the role of Majorana $ ext{π}$ modes, and explains how rung coupling preserves quasienergy spacing against imperfections.

Findings

Presence of subharmonic magnetization dynamics similar to discrete time crystals.

Identification of corner Majorana $ ext{π}$ modes as topological features.

Rung coupling prevents degeneracy, maintaining quasienergy spacing despite imperfections.

Abstract

Studies of periodically driven one-dimensional many-body systems have advanced our understanding of complex systems and stimulated promising developments in quantum simulation. It is hence of interest to go one step further, by investigating the topological and dynamical aspects of periodically driven spin ladders as clean quasi-one-dimensional systems with spin-spin interaction in the rung direction. Specifically, we find that such systems display subharmonic magnetization dynamics reminiscent to that of discrete time crystals (DTCs) at finite system sizes. Through the use of generalized Jordan-Wigner transformation, this feature can be attributed to presence of corner Majorana $\pi$ modes (MPMs), which are of topological origin, in the systems' equivalent Majorana lattice. Special emphasis is placed on how the coupling in the rung direction of the ladder prevents degeneracy from occurring between states differing by a single spin excitation, thus preserving the MPM-induced $\pi/T$ quasienergy spacing of the Floquet eigenstates in the presence of parameter imperfection. This feature, which is absent in their strict one-dimensional counterparts, may yield fascinating consequences in future studies of higher dimensional Floquet many-body systems.