Tensor Networks for Ab Initio Quantum Systems

Tensor Networks for Ab Initio Quantum Systems

Tensor Networks for Ab Initio Quantum Systems a E.M. Stoudenmire Sep 2019 - Jülich This talk: The many-electron problem Tensor networks Intro to quantum chemistry Chemistry approaches for tensor networks The Many-Electron Problem Behavior of electrons in matter: • continuum problem • three dimensional • strong interaction (repulsion) between electrons Credit: MARK GARLICK/SCIENCE PHOTO LIBRARY/Getty Images Can simplify various ways: • Born-Oppenheimer approximation (classical nuclei) • ignore most relativistic effects Figure credit: iqmol.org Then problem simplifies to @ i = Hˆ <latexit 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sha1_base64="a2fXYrGItQikxgAawDxnFLhVb9A=">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</latexit> = one-body potential u(r, r0) = two-body interaction <latexit 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sha1_base64="r8Gtlj9x+Oh2OTr13PrljjI/O2Q=">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</latexit> r 1 − 2 Coulomb repulsion of electrons Accurate ground state energy of electronic structure problem extremely useful Example: energy of two atoms, distance R E R equilibrium bond length R binding energy vibrational frequency Most techniques require discrete and finite system To achieve this can: • integrate out "core" electrons (pseudopotentials) • treat high energy states with approximations

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