Dynamical scaling behavior of the two-dimensional random singlet state in the random <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>Q</mml:mi></mml:math> model

In this work, we study the scaling relation of energy and length scales in the two-dimensional (2D) random singlet (RS) state in the random $Q$ model. To investigate the intrinsic energy scale of the spinon subsystem arising from the model, we develop a constrained subspace update algorithm within the framework of the stochastic series expansion method to extract the singlet-triplet gap of the system. The 2D RS state exhibits scaling behavior similar to the infinite-randomness fixed point, at least within the length scales that we simulate. Furthermore, by rescaling the system size according to the strength of randomness, we observe that the data for the excitation gap and the width of the gap distribution collapse onto a single curve. This implies that a model with different strengths of randomness may correspond to the same fixed point.