Truncation errors in self-similar continuous unitary transformations

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.

17 pages, 8 figures

References in corpus (6)

• Interaction Quench in the Hubbard model
• Emergent Fermions and Anyons in the Kitaev Model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Creation and Manipulation of Anyons in the Kitaev Model
• Systematic Mapping of the Hubbard Model to the Generalized t-J Model
• Derivation of the t-J model for finite doping