Topological phases, Majorana modes and quench dynamics in a spin ladder system

TL;DR

This paper investigates the topological phases and Majorana modes in a spin ladder system by mapping it to a fermionic model, analyzing vortex effects, and exploring quench dynamics across quantum critical points.

Contribution

It introduces a new topological invariant for the Kitaev ladder and connects spin phases with topologically non-trivial fermionic phases, including dynamic quench analysis.

Findings

Vortex patterns enable tuning into topologically non-trivial phases.

A new topological invariant determines Majorana modes at boundaries.

Post-quench dynamics reveal behavior across quantum critical points.

Abstract

We explore the salient features of the `Kitaev ladder', a two-legged ladder version of the spin-1/2 Kitaev model on a honeycomb lattice, by mapping it to a one-dimensional fermionic p-wave superconducting system. We examine the connections between spin phases and topologically non-trivial phases of non-interacting fermionic systems, demonstrating the equivalence between the spontaneous breaking of global Z2 symmetry in spin systems and the existence of isolated Majorana modes. In the Kitaev ladder, we investigate topological properties of the system in different sectors characterized by the presence or absence of a vortex in each plaquette of the ladder. We show that vortex patterns can yield a rich parameter space for tuning into topologically non-trivial phases. We introduce a new topological invariant which explicitly determines the presence of zero energy Majorana modes at the boundaries of such phases. Finally, we discuss dynamic quenching between topologically non-trivial phases in the Kitaev ladder, and in particular, the post-quench dynamics governed by tuning through a quantum critical point.