Eur. Phys. J. B 79, 225-240 (2011)
https://doi.org/10.1140/epjb/e2010-10723-6

Truncation errors in self-similar continuous unitary transformations

Lehrstuhl für Theoretische Physik I, Dortmund University of Technology, Otto-Hahn Straße 4, 44221 Dortmund, Germany

Corresponding authors: ^a drescher@fkt.physik.tu-dortmund.de - ^b fischer@fkt.physik.tu-dortmund.de - ^c uhrig@fkt.physik.tu-dortmund.de

Received: 18 September 2010
Revised: 27 October 2010
Published online: 21 December 2010

Abstract

Effects of truncation in self-similar continuous unitary transformations (S-CUT) are estimated rigorously. We find a formal description via an inhomogeneous flow equation. In this way, we are able to quantify truncation errors within the framework of the S-CUT and obtain rigorous error bounds for the ground state energy and the highest excited level. These bounds can be lowered exploiting symmetries of the Hamiltonian. We illustrate our approach with results for a toy model of two interacting hard-core bosons and the dimerized S = 1/2 Heisenberg chain.