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 renormalization group (SDRG) method. The system consists of S = 1/2 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 of rP ≃ 0.94 and reproduces the entanglement entropy S(ℓ) in excellent quantitative agreement with SDRG across all subsystem sizes and interaction exponents. RG-flow heatmaps confirm that the GNN learns the sequential decimation hierarchy rather than merely fitting final- state observables. Finite-temperature entanglement properties are incorporated via the SDRG-X 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 SDRG-X and analytical predictions without retraining.