# Emergent phases in a compass chain with multisite interactions

## TL;DR

This paper investigates a dimerised spin chain with three-site interactions, revealing topological Majorana modes, a BKT quantum phase transition to a spin liquid phase, and the role of quantum correlations in signaling these transitions.

## Contribution

It introduces the effects of three-site interactions on topological and exotic phases in a spin chain, including the emergence of a BKT transition and the robustness of the spin liquid phase.

## Key findings

- Zero-energy Majorana modes depend on the Pfaffian sign and topological invariant.
- A BKT transition leads to a spin liquid phase with dynamic exponent z=4.
- Quantum discord and relative entropy can detect the BKT transition.

## Abstract

We study a dimerised spin chain with biaxial magnetic interacting ions in the presence of an externally induced three-site interactions out of equilibrium. In the general case, the three-site interactions play a role in renormalizing the effective uniform magnetic field. We find that the existence of zero-energy Majorana modes is intricately related to the sign of Pfaffian of the Bogoliubov-de Gennes Hamiltonian and the relevant $Z_2$ topological invariant. In contrast, we show that an exotic spin liquid phase can emerge in the compass limit through a Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition. Such a BKT transition is characterized by a large dynamic exponent $z=4$, and the spin-liquid phase is robust under a uniform magnetic field. We find the relative entropy and the quantum discord can signal the BKT transitions. We also uncover a few differences in deriving the correlation functions for the systems with broken reflection symmetry.