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Entanglement entropy on a fuzzy sphere : matrix quantum mechanics simulations using deep learning Andrzejewski, Tomasz


The Ryu-Takayanagi formula, discovered in the context of the AdS/CFT correspondence, revealed that entanglement entropy encodes the information about geometry. In order to learn about non-locality structure of QFTs on fuzzy spaces we calculate entanglement entropy and mutual information for a massive free scalar field on a noncommutative (fuzzy) sphere, using standard methods for finding entropy of coupled harmonic oscillators. When computing these quantities we use two different methods of factorizing quantum mechanical Hilbert spaces, i.e. two different constructions of projection matrices. We find that our results are largely dependent on which projection matrix we used. We further use machine learning techniques to find variational wavefunction for scalar field theory with a quartic interaction on a fuzzy sphere. The theory is realized by a matrix model, where the matrix size plays the role of an ultraviolet cutoff. We use variational quantum Monte Carlo with deep generative flows to search for ground state energy of this matrix model. We find that, depending on the projection matrix used, entropy stays the same or behaves differently as we vary the parameter of quartic interaction.

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