Valence Bond Glass and Glassy Spin Liquid in Disordered Frustrated Magnets

The absence of conventional magnetic order together with anomalous low-temperature magnetic heat capacity is often interpreted as evidence for quantum spin liquid ground states in frustrated magnets. Using a recently developed semiclassical Monte Carlo approach, we show that similar thermodynamic signatures arise in the highly frustrated regime of the disordered spin-1/2 J1-J2 Heisenberg model on the square lattice. By analyzing the freezing parameters, the distribution of spin-spin correlations, and the specific heat, we identify the ground state as a valence-bond glass that melts into a glassy spin liquid at finite temperatures. We show that the low-temperature specific-heat anomaly originates from collective singlet excitations, and consequently it is insensitive to external magnetic fields. This leads to a robust experimental signature of the valence bond glass phase and a completely new interpretation of the thermodynamic data on disordered spin-liquid candidate materials.