Magnon Bose-Einstein Condensation in a Heavy Fermion Metal

Recent experiments on heavy fermion materials have revealed a range of compounds that are both metallic and have local magnetic moments that reside on geometrically frustrated lattices. An interesting example of frustration, realized in a number of materials, is provided by systems with a valence bond solid ground state, which exhibit a magnetic transition in the same universality class as Bose-Einstein condensation (BEC) in an applied magnetic field. Moreover, recent experiments on YbAl₃C₃ suggest that this compound may realize a magnon BEC transition in the presence of an itinerant conduction band. Motivated by these observations, we consider a one-dimensional two-leg spin ladder with a valence bond solid ground state doped with itinerant fermions. Using the Density Matrix Renormalization Group we study the system as a function of Kondo coupling, magnetic field and the density of itinerant fermions. In addition, we use analytical techniques to map out the phase diagram and study the critical properties, and compare limiting cases with the numerically exact DMRG results. We also discuss the application of our results to 2D and 3D systems.