Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction

TL;DR

This paper explores the coexistence of strong and weak Majorana zero modes in an anisotropic XY spin chain with second-neighbor interactions, revealing new topological phases and potential experimental realizations.

Contribution

It introduces the topological phase diagram of the anisotropic XY spin chain with second-neighbor interactions, identifying the coexistence of multiple Majorana zero modes including weak modes.

Findings

Coexistence of multiple Majorana zero modes confirmed.

Identification of weak zero modes restricted to a Hilbert subspace.

Potential for experimental realization in quantum spin materials and cold atom systems.

Abstract

We theoretically investigate Majorana zero modes emerging in an anisotropic XY spin chain with second neighbor interactions. The spin chain is mathematically equivalent to the Kitaev chain composing of spinless fermions if only nearest-neighbor interactions are considered. Recent studies on the Kitaev chain with long-ranged interactions, have presented coexistence of several Majorana zero modes. Investigating the topological phase diagram of the anisotropic XY spin chain with second neighbor interactions, we find coexistence of several Majorana zero modes similar to the Kitaev chain. However, we confirm that one of zero modes is restricted into a Hilbert subspace. The mode is regarded as a so-called weak zero mode that should exhibit thermodynamical properties different from a (strong) zero mode appearing in the whole Hilbert space. Since the quantum statistics of spin is the same as a hard-core boson, we expect an experimental realization of the weak mode in not only quantum spin materials but also optical lattices for cold atom systems.