2017/11/30 by Claudius Hubig, C. Hubig, Jutho Haegeman +3
Mathematics · Physics and Astronomy · #Combinatorics #Extrapolation #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Measure (data warehouse) #Physics #Physics of Superconductivity and Magnetism #Product (mathematics) #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Truncation error #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.97.045125
published as Phys. Rev. B 97, 045125 (2018) · 10 pages, 11 figures
arxiv created 2018/01/03 · openalex publication_date 2018/01/16 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce an error measure for matrix-product states without requiring the relatively costly two-site density-matrix renormalization group (2DMRG). This error measure is based on an approximation of the full variance \ensuremath⟨\ensuremathψ|(\stackrel\ifmmode \else \\fiH\ensuremath-E)2|\ensuremathψ\ensuremath⟩. When applied to a series of matrix-product states 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 \ensuremath⟨\ensuremathψ|\stackrel\ifmmode \else \\fiH|\ensuremathψ\ensuremath⟩ and a trivially parallelized part scaling like a single operator application in 2DMRG. The reliability of this error measure is demonstrated by four examples: the L=30,S=1/2 Heisenberg chain, the L=50 Hubbard chain, an electronic model with long-range Coulomb-like interactions, and the Hubbard model on a cylinder with a size of 10\ifmmode×\else\texttimes\fi4. Extrapolation in this error measure is shown to be on par with extrapolation in the 2DMRG truncation error or the full variance \ensuremath⟨\ensuremathψ|(\stackrel\ifmmode \else \\fiH\ensuremath-E)2|\ensuremathψ\ensuremath⟩ at a fraction of the computational effort.