$Z_{2}$ order fractionalization, topological phase transition, and odd frequency pairing in an exactly solvable spin-charge ladder

TL;DR

This paper introduces an exactly solvable spin-charge ladder model that exhibits $Z_{2}$ order fractionalization, topological phase transitions, and odd-frequency pairing, providing insights into fractionalized topological states and Majorana excitations.

Contribution

It presents a novel exactly solvable model combining spin and charge degrees of freedom to study order fractionalization and topological transitions with explicit solutions.

Findings

Revealed $Z_{2}$ order fractionalization with dual symmetry breaking.

Identified a topological superconductor phase with gapped $Z_{2}$ Kondo flux excitations.

Demonstrated Majorana spinons inducing odd-frequency pairing in the superconducting wire.

Abstract

Motivated by the order fractionalization in Kitaev-Kondo model, we propose an exactly solvable spin-charge ladder model to study the order fractionalization with discrete symmetry. The spin-charge ladder is composed of a spin chain and a superconducting wire coupled via an Ising-type interaction, and we obtain the exact solution in the flat band limit. The exact solution reveals the $Z_{2}$ order fractionalization with dual symmetry breaking and intertwined order parameters. We investigate the topological phase transition of the spin-charge ladder via the spectral chiral index, and identify the correlated topological superconductor (TSC*) phase with gapped $Z_{2}$ Kondo flux excitations. We demonstrate Majorana spinons generated odd frequency pairing in the superconducting wire. We also discuss the order fractionalization in the perspective of $Z_{2}$ lattice gauge theory.