Deep Quantum Geometry of Matrices
Autor: | Sean A. Hartnoll, Xizhi Han |
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Rok vydání: | 2019 |
Předmět: |
Physics
High Energy Physics - Theory Quantum geometry Entropy (statistical thermodynamics) QC1-999 General Physics and Astronomy Semiclassical physics FOS: Physical sciences Quantum entanglement 01 natural sciences 010305 fluids & plasmas Matrix (mathematics) High Energy Physics - Theory (hep-th) 0103 physical sciences 010306 general physics Wave function Quantum Mathematical physics Fuzzy sphere |
Zdroj: | Physical Review X, Vol 10, Iss 1, p 011069 (2020) |
DOI: | 10.48550/arxiv.1906.08781 |
Popis: | We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to search for gauge invariant low energy states. The ground state, and also long-lived metastable states, of an $\mathrm{SU}(N)$ matrix quantum mechanics with three bosonic matrices, as well as its supersymmetric `mini-BMN' extension, are studied as a function of coupling and $N$. Known semiclassical fuzzy sphere states are recovered, and the collapse of these geometries in more strongly quantum regimes is probed using the variational wavefunction. We then describe a factorization of the quantum mechanical Hilbert space that corresponds to a spatial partition of the emergent geometry. Under this partition, the fuzzy sphere states show a boundary-law entanglement entropy in the large $N$ limit. Comment: 36+26 pages. 16 Figs. v2: added results on small nu limit. Code available online: https://github.com/hanxzh94/matrix-model |
Databáze: | OpenAIRE |
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