Quasiparticle-continuum level repulsion in a quantum magnet

A neutron scattering study of the quantum magnet BiCu 2 PO 6 demonstrates a phenomenon known as energy-level repulsion, which occurs between a long-lived quasiparticle state and a many-particle continuum. When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided 1 . Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids 2 . However, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum 3 , 4 , 5 . Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu 2 PO 6 , we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states.