Topological Edge Modes in the Many-Body Spectrum of a Ladder Quantum Paramagnet

We investigate the excitations of a quantum paramagnet on a one-dimensional ladder, and show that by applying an external magnetic field a topological phase transition is enforced. Because the triplon excitations of the ladder are gapped, the scattering and decay phase space is much smaller than in spin wave spectra, and the topological excitations are more robust. We demonstrate the emergence of surface modes at the end of the ladder and show their stability over large portions of the phase diagram, even when many-body interaction are included, which we treat using Density Matrix Renomarmalization Group and Time Evolution Methods.

We classify the topological phases by the winding of the many-body wavefunction and its quantum entanglement encoded in the Fisher information. We further relate our model to the quasi one-dimensional quantum antiferromagnet BiCu₂PO₆, discuss the material's potential applications, as well as how the emergent surface modes can be experimentally realized and detected.