From Classical to Quantum: Extending Prometheus to Uncover Quantum Critical Behavior in Disordered Transverse Field Ising Chains

From Classical to Quantum: Extending Prometheus to Uncover Quantum Critical Behavior in Disordered Transverse Field Ising Chains | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article From Classical to Quantum: Extending Prometheus to Uncover Quantum Critical Behavior in Disordered Transverse Field Ising Chains Brandon Yee, Wilson Collins, Maximilian Rutkowski This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8283039/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract We extend the Prometheus framework from classical to quantum phase transitions, demonstrat- ing unsupervised discovery of quantum critical phenomena in the disordered transverse field Ising model (DTFIM). Building upon our previous work on classical spin systems [1, 2], we develop a quantum-aware variational autoencoder (Q-VAE) architecture that operates directly on quantum ground state wavefunctions obtained via exact diagonalization. The Q-VAE learns latent represen- tations that capture the essential physics of the quantum phase transition between paramagnetic and ferromagnetic phases, achieving detection of the quantum critical point hc = 1.00 ± 0.02 in the clean limit, consistent with the theoretical value hc/J = 1. We introduce disorder through random transverse fields h i ∼ Uniform[h−W, h+W ] and investigate the disorder-driven infinite-randomness fixed point characteristic of the random TFIM. Our framework successfully identifies the shift in critical behavior with increasing disorder strength and extracts effective critical exponents through finite-size scaling analysis. We formulate and test the hypothesis that the Q-VAE latent space structure reflects the activated dynamical scaling ln ξ ∼ |h − hc| −ψ with ψ ≈ 0.5 expected at the infinite-randomness fixed point. The Prometheus quantum discovery pipeline provides a systematic approach to exploring quantum phase diagrams in systems where analytical solutions are unavail- able, with potential applications to quantum materials, cold atom systems, and quantum computing platforms. Computational Physics Hard Condensed-matter Physics Soft Condensed-matter Physics Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Building upon our previous work on classical spin systems [1, 2], we develop a quantum-aware variational autoencoder (Q-VAE) architecture that operates directly on quantum ground state wavefunctions obtained via exact diagonalization. The Q-VAE learns latent represen- tations that capture the essential physics of the quantum phase transition between paramagnetic and ferromagnetic phases, achieving detection of the quantum critical point hc = 1.00 ± 0.02 in the clean limit, consistent with the theoretical value hc/J = 1. We introduce disorder through random transverse fields h\u003csub\u003ei\u003c/sub\u003e ∼ Uniform[h−W, h+W ] and investigate the disorder-driven infinite-randomness fixed point characteristic of the random TFIM. Our framework successfully identifies the shift in critical behavior with increasing disorder strength and extracts effective critical exponents through finite-size scaling analysis. We formulate and test the hypothesis that the Q-VAE latent space structure reflects the activated dynamical scaling ln ξ ∼ |h − hc| \u003csup\u003e−ψ\u003c/sup\u003e with ψ ≈ 0.5 expected at the infinite-randomness fixed point. 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