Hubig, C.; Haegeman, J.; Schollwoeck, U.
(2018):
Error estimates for extrapolations with matrixproduct states.
In: Physical Review B, Vol. 97, No. 4, 45125

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Abstract
We introduce an error measure for matrixproduct states without requiring the relatively costly twosite densitymatrix renormalization group (2DMRG). This error measure is based on an approximation of the full variance <psi broken vertical bar(H) over cap  E)(2) broken vertical bar psi >. When applied to a series of matrixproduct states at different bond dimensions obtained from a singlesite densitymatrix renormalization group (1DMRG) calculation, it allows for the extrapolation of observables towards the zeroerror 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 <psi broken vertical bar(H) over cap broken vertical bar psi > 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 longrange Coulomblike interactions, and the Hubbard model on a cylinder with a size of 10 x 4. Extrapolation in this error measure is shown to be on par with extrapolation in the 2DMRG truncation error or the full variance <psi broken vertical bar(H) over cap  E)(2) broken vertical bar psi > at a fraction of the computational effort.