Truncation errors in self-similar continuous unitary transformations

TL;DR

This paper rigorously analyzes truncation errors in self-similar continuous unitary transformations, providing error bounds for physical quantities and demonstrating the approach on specific quantum models.

Contribution

It introduces a formal inhomogeneous flow equation to estimate and bound truncation errors within S-CUT, enhancing the method's reliability.

Findings

Rigorous error bounds for ground state energy and excited levels.

Truncation errors can be quantified and reduced using symmetries.

Application to toy model and Heisenberg chain demonstrates effectiveness.

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.