Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets

• Published in: Physical review. X Vol. 8; no. 4; p. 041040
• Main Authors: Liu, Lu, Shao, Hui, Lin, Yu-Cheng, Guo, Wenan, Sandvik, Anders W.
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 05-12-2018
• Subjects: Antiferromagnetism; Correlation; Dilution; Domain walls; Fixed points (mathematics); Inelastic scattering; Lattices (mathematics); Magnetic permeability; Magnetic properties; Magnets; Material properties; Phase transitions; Physical properties; Power law; Randomness; Simulation; Subgroups; Thermodynamic properties; Two dimensional models
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.8.041040

We study the effects of disorder (quenched randomness) in a two-dimensional square-latticeS=1/2quantum-spin system, theJ−Qmodel with a multispin interactionQsupplementing the Heisenberg exchangeJ. In the absence of disorder, the system hosts antiferromagnetic (AFM) and columnar valence-bond-solid (VBS) ground states. The VBS breaksZ4symmetry 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-Jor -Qinteractions 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 asr−2as a function of distancer. 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 exponentzis finite in two dimensions. By studying quantum-critical scaling of the magnetic susceptibility, we find thatzvaries, taking the valuez=2at 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 magnetsSr2CuTe1−xWxO6forxin the range of 0.2–0.5.