# Topological quantum paramagnet in a quantum spin ladder

## TL;DR

This paper demonstrates that triplon excitations in a quantum spin ladder can exhibit topologically nontrivial phases in the quantum-disordered paramagnetic state, with transitions tunable by magnetic fields and observable via edge states.

## Contribution

It reveals topological properties of triplon excitations in a quantum spin ladder's paramagnetic phase, including a field-tunable topological transition and associated edge states.

## Key findings

- Identification of topologically distinct triplon phases
- Derivation of the winding number for triplon topology
- Prediction of localized edge states in the topological phase

## Abstract

It has recently been found that bosonic excitations of ordered media, such as phonons or spinons, can exhibit topologically nontrivial band structures. Of particular interest are magnon and triplon excitations in quantum magnets, as they can easily be manipulated by an applied field. Here we study triplon excitations in an S=1/2 quantum spin ladder and show that they exhibit nontrivial topology, even in the quantum-disordered paramagnetic phase. Our analysis reveals that the paramagnetic phase actually consists of two separate regions with topologically distinct triplon excitations. We demonstrate that the topological transition between these two regions can be tuned by an external magnetic field. The winding number that characterizes the topology of the triplons is derived and evaluated. By the bulk-boundary correspondence, we find that the non-zero winding number implies the presence of localized triplon end states. Experimental signatures and possible physical realizations of the topological paramagnetic phase are discussed.