Observation of a symmetry-protected topological phase in external magnetic fields

TL;DR

This paper reports the real-space observation of a symmetry-protected topological phase in interacting nuclear spins and investigates the transition between topologically distinct phases using many-body Chern numbers derived from dynamical responses to magnetic fields.

Contribution

It demonstrates a method to directly characterize topological features of quantum many-body states via external magnetic field manipulation and measurement of many-body Chern numbers.

Findings

Observation of a topological phase with interacting nuclear spins

Measurement of a many-body Chern number close to 2

Identification of a transition between topologically distinct phases

Abstract

Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological phases requires the robust topological invariants, whereas measuring these global quantities presents an outstanding challenge for experiments, especially in interacting systems. Here we report the real-space observation of a symmetry-protected topological phase with interacting nuclear spins, and probe the interaction-induced transition between two topologically distinct phases, both of which are classified by many-body Chern numbers obtained from the dynamical response to the external magnetic fields. The resulting value of Chern number ($\bar{\mathcal{C}h} = 1.958 \pm 0.070$) demonstrates the robust ground state degeneracy, and also determines the number of nontrivial edge states. Our findings enable direct characterization of topological features of quantum many-body states through gradually decreasing the strength of the introduced external fields.