Characterizing random-singlet state in two-dimensional frustrated quantum magnets and implications for the double perovskite Sr\(_2\)CuTe\(_{1-x}\)W\(_{x}\)O\(_6\)

Abstract

Motivated by the recent experimental observations of spin-liquid-like behaviors in the compound double perovskite Sr\(_2\)CuTe\(_{1-x}\)W\(_{x}\)O\(_6\), which realizes the simultaneous tuning of frustration and disorder, we study the spin-\(1/2\) Heisenberg model with the randomly distributed nearest-neighbor (\(J_1\)) and next-nearest-neighbor (\(J_2\)) interactions on the square lattice. By using the large-scale density matrix renormalization group (DMRG) calculation on cylinder system with circumference up to \(10\) lattice sites, we identify a disordered phase between the N\'eel and the stripe magnetic order phase with growing ratio \(J_2 / J_1\) in the strong randomness regime. The vanished spin-freezing parameter indicates the absent spin glass order in this disordered phase. The large-size DMRG results unveil that the spin-freezing parameter decays with system length \(L_x\) as \(L^{-1/2}_x\) and the mean spin correlation decays as \(r^{-2}\) as a function of distance \(r\), which follow the same size dependences in the one-dimensional random singlet (RS) state. We propose this disordered state as a two-dimensional analog of the RS state in one dimension. The analysis of the formed different clusters in this RS state demonstrates the existence of the orphan spins, which may account for the gapless excitations. Our results indicate that this RS state may belong to the same fixed point as the RS state found in the random \(J-Q\) model, and the large-scale DMRG simulation opens new opportunities for further studies on frustrated antiferromangets with disorder. We also discuss the implications of our results for understanding the spin-liquid-like compound Sr\(_2\)CuTe\(_{1-x}\)W\(_{x}\)O\(_6\).