Enhanced Perturbative Continuous Unitary Transformations

TL;DR

This paper introduces an enhanced perturbative continuous unitary transformation (epCUT) method that extends the applicability of pCUT to non-equidistant spectra, enabling more efficient and robust data extraction for complex quantum systems.

Contribution

It develops a new epCUT approach that handles non-equidistant spectra and provides a numerical scheme for extracting data from flow equations.

Findings

Successfully applied to harmonic oscillator with quartic perturbation.

Effective for two-leg spin ladders with non-equidistant spectra.

Demonstrates robustness and efficiency of the numerical integration scheme.

Abstract

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary transformation (pCUT) among others. So far, this approach required an equidistant unperturbed spectrum. Here, we pursue two goals: First, we extend its applicability to non-equidistant spectra with the particular focus on an efficient derivation of the differential flow equations, which define the enhanced perturbative continuous unitary transformation (epCUT). Second, we show that the numerical integration of the flow equations yields a robust scheme to extract data from the epCUT. The method is illustrated by the perturbation of the harmonic oscillator with a quartic term and of the two-leg spin ladders in the strong-rung-coupling limit for uniform and alternating rung couplings. The latter case provides an example of perturbation around a non-equidistant spectrum.