13 research outputs found
Enhanced Perturbative Continuous Unitary Transformations
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.Comment: 27 pages, 18 figures; separated methodological background from
introduction, added perturbed harmonic oscillator for additional
illustration, added explicit solution of deepCUT equation
Communication: Generalized canonical purification for density matrix minimization
A Lagrangian formulation for the constrained search for the N-representable one-particle density matrix based on the McWeeny idempotency error minimization is proposed, which converges systematically to the ground state. A closed form of the canonical purification is derived for which no a posteriori adjustment on the trace of the density matrix is needed. The relationship with comparable methods is discussed, showing their possible generalization through the hole-particle duality. The appealing simplicity of this self-consistent recursion relation along with its low computational complexity could prove useful as an alternative to diagonalization in solving dense and sparse matrix eigenvalue problems
Transient analysis of Markov-fluid-driven queues
Queueing systems, Markov fluid, Transient analysis, 60K20, 62J10, 60J25,