Scaling in RG Flows of Disordered Quantum Spin Systems

Several longstanding problems in spin-1/2 quantum magnetism concern quenched disorder. In this talk I will discuss the role of random exchange energies in spin-1/2 magnets where magnetic frustration promotes the formation of entangled valence bonds. Results include a theory of 2D valence-bond-solids subject to weak bond randomness, and an instability of classical dimer models that is applicable to strongly disordered spin liquids. In both cases we find that bond disorder nucleates topological defects that carry spin-1/2 moments, thereby renormalizing the lattice into a strongly random spin network with interesting low-energy excitations. The results lead to conjectures, and a proof in 1D, of Lieb-Schultz-Mattis-type restrictions for disordered magnets with spin-1/2 per statistical unit cell. I will then turn to experimental connections: most strikingly, recent heat capacity data of multiple magnetic materials -- all with frustration and disorder but no other common relation -- nevertheless all show quasi-universal one-parameter data collapse of C[H,T] in a magnetic field. I will show how this data collapse and its scaling function can be understood in terms of the theory as an emergent network of long range valence bonds at low energies. If time permits I will also re-interpret this theory in terms of quantum anomalies and connect to other 2D anomalies of 3D topological states.