Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets

We study the effects of disorder (quenched randomness) in a two-dimensional square-lattice S =1 /2 quantum-spin system, the J -Q model with a multispin interaction Q supplementing the Heisenberg exchange J . In the absence of disorder, the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaks Z₄ symmetry spontaneously, and in the presence of arbitrarily weak disorder it forms domains. Using quantum Monte Carlo simulations, we demonstrate two different kinds of such disordered VBS states. Upon dilution, a removed site in one sublattice forces a leftover localized spin in the opposite sublattice. Such spins interact through the host system and always form AFM order. In the case of random-J or -Q interactions in the intact lattice, we find a different spin-liquid-like state with no magnetic or VBS order but with algebraically decaying mean correlations. Here we identify localized spinons at the nexus of domain walls separating regions with the four different VBS patterns. These spinons form correlated groups with the same number of spinons and antispinons. Within such a group, we argue that there is a strong tendency to singlet formation because of the native pairing and relatively strong spinon-spinon interactions mediated by the domain walls. Thus, the spinon groups are effectively isolated from each other and no long-range AFM order forms. The mean spin correlations decay as r^-2 as a function of distance r . We propose that this state is a two-dimensional analogue of the well-known random-singlet (RS) state in one dimension, though, in contrast to the one-dimensional case the dynamic exponent z is finite in two dimensions. By studying quantum-critical scaling of the magnetic susceptibility, we find that z varies, taking the value z =2 at the AFM-RS phase boundary and growing upon moving into the RS phase (thus, causing a power-law divergent susceptibility). The RS state discovered here in a system without geometric frustration may correspond to the same fixed point as the RS state recently proposed for frustrated systems, and the ability to study it without Monte Carlo sign problems opens up opportunities for further detailed characterization of its static and dynamic properties. We also discuss experimental evidence of the RS phase in the quasi-two-dimensional square-lattice random-exchange quantum magnets Sr₂ CuTe_{1 -x}W_x O₆ for x in the range of 0.2-0.5.