Papers › Error estimates for extrapolations with matrix-product states
Error estimates for extrapolations with matrix-product states
C. Hubig, J. Haegeman, U. Schollwöck
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We introduce a new 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 ⟨ψ| ( Ĥ - E )² |ψ⟩. 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 ⟨ψ| Ĥ | ψ⟩ and a trivially parallelized part scaling like a single operator application in 2DMRG. The reliability of the new error measure is demonstrated at 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 of size 10 ×4. 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.
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