Machine Learning the Strong Disorder Renormalization Group Method for Disordered Quantum Spin Chains

We train machine learning algorithms to infer the entanglement structure of disordered long-range interacting quantum spin chains by learning from the strong disorder renormalisation group (SDRG) method. The system consists of S=1/2-quantum spins coupled by antiferromagnetic power-law interactions with decay exponent α at random positions on a one-dimensional chain. Using SDRG as a physics-informed teacher, we compare a Random Forest classifier as a classical baseline with a graph neural network (GNN) that operates directly on the interaction graph and learns a bond-ranking rule mirroring the SDRG decimation policy. The GNN achieves a disorder-averaged pairing accuracy close to one and reproduces the entanglement entropy S\(ell\) in excellent quantitative agreement with SDRG across all subsystem sizes and interaction exponents. RG flow heat maps confirm that the GNN learns the sequential decimation hierarchy rather than merely fitting final-state observables. Finite-temperature entanglement properties are incorporated via the SDRGX framework through a two-stage strategy, using the zero-temperature GNN to generate the RG flow and sampling thermal occupations from the canonical ensemble, yielding results in agreement with both numerical SDRGX and analytical predictions without retraining.