Enhanced perturbative continuous unitary transformations

H. Krull, N. A. Drescher, and G. S. Uhrig
Phys. Rev. B 86, 125113 – Published 10 September 2012

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 nonequidistant 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 nonequidistant spectrum.

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  • Received 14 February 2012

DOI:https://doi.org/10.1103/PhysRevB.86.125113

©2012 American Physical Society

Authors & Affiliations

H. Krull*, N. A. Drescher, and G. S. Uhrig

  • Lehrstuhl für Theoretische Physik I, Technische Univerität Dortmund, Otto-Hahn Straße 4, 44221 Dortmund, Germany

  • *holger.krull@tu-dortmund.de
  • nils.drescher@tu-dortmund.de
  • goetz.uhrig@tu-dortmund.de

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Issue

Vol. 86, Iss. 12 — 15 September 2012

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