Data collapse and scaling theory of frustration and disorder in quantum magnets

Several longstanding problems in quantum magnetism concern quenched disorder. I will analyze the role of random exchange energies in spin-1/2 magnets where magnetic frustration promotes the formation of entangled valence bonds. This includes a theory for 2d valence-bond solids subject to weak bond randomness as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. In both cases, we find that bond-randomness 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. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions for disordered magnets with spin-1/2 per statistical unit cell. I will also discuss predictions for various experimental observables and relation to YbMgGaO4 and YbZnGaO4. As an especially interesting application, I'll discuss heat capacity measurements on the magnets H3LiIr2O6, LiZn2Mo3O8, ZnCu3(OH)6Cl2 and 1T-TaS2 -- all described by magnetic frustration and quenched disorder but with no other common relation -- that nevertheless show apparently universal one-parameter data collapse of C[H,T] in a magnetic field. I will argue that this data collapse and its particular scaling function can be understood in terms of the theory, as an emergent network of long range valence bonds at low energies.