Berlin 2018 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 94: Correlated Electrons: Other Theoretical Topics
TT 94.11: Vortrag
Donnerstag, 15. März 2018, 18:00–18:15, H 3010
Error estimates for extrapolations with matrix-product states — •Claudius Hubig1,2, Jutho Haegeman3, and Ulrich Schollwöck1 — 1Department of Physics, Ludwig-Maximilians-Universität München, Germany — 2Max-Planck-Institut für Quantenoptik, Garching, Germany — 3Department of Physics and Astronomy, Ghent University, Ghent, Belgium
We introduce a new error measure for matrix-product states (MPS) based on an approximation of the full variance ⟨ ψ | ( Ĥ − E )2 |ψ ⟩. When applied to a series of MPS at different bond dimensions obtained from a single-site density matrix renormalization group (1DMRG) calculation, it allows for the extrapolation of observables towards the zero-error case representing the exact ground state of the system.
The calculation of the error measure is split into a sequential part of cost equivalent to two calculations of ⟨ ψ | Ĥ | ψ ⟩ and a trivially parallelized part scaling like a single operator application in two-site DMRG (2DMRG). The reliability of the new error measure is demonstrated at four examples and extrapolation in the new error measure is shown to be on-par with extrapolation in the 2DMRG truncation error or the full variance ⟨ ψ | ( Ĥ − E )2 |ψ ⟩ at a fraction of the computational effort.
arxiv.org/abs/1711.01104