Funktionaalirenormalisaatioryhmämenetelmän sovellus kvanttispin-ketjuille
Year: 2011
Type: dissertation
Abstract: In this thesis, the functional renormalization group (FRG) method is applied to quantum spin chains. FRG is a well-known method in the treatment of correlated fermion systems, but the method has been applied to spin systems only recently[1]. The method has been used, however, only as a qualitative tool to find phase boundaries for frustrated spin systems with multiple competing interactions. The main goal of this work is to critically assess the general accuracy of the method by studying toy models, for which quantitative comparison with exact results is possible. After a full derivation of the flow equations for spin systems, the numerical solution of the resulting non-linear system of differential equations is presented. It is shown that in the antiferromagnetic two-site Heisenberg model, FRG can reproduce some known properties of the singlet state but the ground state energy, for example, disagrees with the exact result by 36 %. In addition, the quasiparticle self-energy and dynamic spin-spin correlation functions are of an incorrect form. Unphysical fluctuations in the particle number are shown to be large. In the antiferromagnetic Heisenberg chain, it is shown that whereas the use of properly truncated flow equations regularizes the unphysical antiferromagnetic instability, the resulting ground state is disordered and not critical as expected. [1] J. Reuther and P. Wölfle, Phys. Rev. B 81, 144410 (2010).
Source: Aaltodoc (Aalto University)
Author: Sääskilahti, Kimmo
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7112419782