Dynamical scaling behavior of the two-dimensional random singlet state in the random $Q$ model

TL;DR

This paper investigates the scaling behavior of energy and length scales in the two-dimensional random singlet state of the random Q model, revealing IRFP-like behavior and universality across different randomness strengths.

Contribution

It introduces a constrained subspace update algorithm within SSE to accurately extract the singlet-triplet gap and demonstrates the universality of the fixed point in the 2D RS state.

Findings

Scaling behavior similar to IRFP observed

Data collapse of excitation gap and gap distribution

Universality across different randomness strengths

Abstract

In this work, we study the scaling relation of energy and length scales in the 2D random-singlet (RS) state of 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 (SSE) to extract the singlet-triplet gap of the system. The 2D RS state exhibits scaling behavior similar to the infinite randomness fixed point (IRFP), 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 the model with different strengths of randomness may correspond to the same fixed point.