arXiv subjects

Maximilian Rutkowski

Publications and source records attributed to Maximilian Rutkowski.

2 recordsLinked to original sources

arXiv2026

Unsupervised Discovery of Intermediate Phase Order in the Frustrated $J_1$-$J_2$ Heisenberg Model via Prometheus Framework

The spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice exhibits a debated intermediate phase between N\'eel antiferromagnetic and stripe ordered regimes, with competing theories proposing plaquette valence bond, nematic, and quantum spin liquid ground states. We apply the Prometheus variational autoencoder framework -- previously applied to classical (2D, 3D Ising) and quantum (disordered transverse field Ising) phase transitions -- to systematically explore the $J_1$-$J_2$ phase diagram using a multi-scale approach. For $L=4$, we employ exact diagonalization with full wavefunction analysis via quantum-aware VAE. For larger systems ($L=6, 8$), we introduce a reduced density matrix (RDM) based methodology using DMRG ground states, enabling scaling beyond the exponential barrier of full Hilbert space representation. Through dense parameter scans of $J_2/J_1 \in [0, 1]$ and comprehensive latent space analysis, we identify the structure factor $S(\pi,\pi)$ and $S(\pi,0)$ as the dominant order parameters discovered by the VAE, with correlations exceeding $|r| > 0.97$. The RDM-VAE approach successfully captures the N\'eel-to-stripe crossover near $J_2/J_1 \approx 0.5$--$0.6$, demonstrating that local quantum correlations encoded in reduced density matrices contain sufficient information for unsupervised phase discovery. This work establishes a scalable pathway for applying machine learning to frustrated quantum systems where full wavefunction access is computationally prohibitive.

cond-mat.str-el↗

arXiv2026

From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems

We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D Ising model student abstract [Yee et al., 2026], we address two fundamental questions: (1) Does the framework scale to higher dimensions where exact solutions are unavailable? (2) Can it generalize to quantum phase transitions driven by quantum fluctuations rather than thermal fluctuations? For the 3D Ising model on lattices up to $L{=}32$, we achieve critical temperature detection within 0.01\% of literature values ($\Tc/J = 4.511 \pm 0.005$) and extract critical exponents with ${\geq}70\%$ accuracy, with statistical analysis correctly identifying the 3D Ising universality class ($p = 0.72$). For quantum systems, we develop quantum-aware VAE (Q-VAE) architectures operating on complex-valued wavefunctions with fidelity-based loss functions, achieving 2\% accuracy in quantum critical point detection for the transverse field Ising model. For the disordered TFIM, we perform a consistency check of activated dynamical scaling $\ln \xi \sim |h - \hc|^{-\psi}$, extracting tunneling exponent $\psi = 0.48 \pm 0.08$ consistent with theoretical predictions ($\psi = 0.5$, $\Delta\chi^2 = 12.3$, $p < 0.001$). This demonstrates that unsupervised learning can identify qualitatively different \emph{types} of critical behavior, serving as a consistency check on known IRFP physics.

cond-mat.dis-nn↗