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Correlations in low-dimensional quantum many-particle systems

Abstract
This thesis concerns correlation effects in quantum many-particle systems in one and two dimensions. Such systems show many exotic non-Fermi liquid phenomena, which can be treated analytically using non-perturbative field-theory methods. Quantum phase transitions between topologically ordered phases of matter, which do not break any symmetries, are studied. It is shown that although there is no local order parameter, a local measure from quantum information theory called reduced fidelity can detect such transitions. Entanglement in quantum impurity systems is also studied. The general expression for scaling corrections in entanglement entropy from boundary perturbations is derived within conformal field theory, showing that the asymptotic decay of Kondo screening clouds follow the same power-law as the impurity specific heat. Furthermore, the effects from spin-orbit interactions on Kondo physics in helical Luttinger liquids are studied. Such helical liquids occur on the edges of two-dimensional topological insulators. It is shown that Rashba and Dresselhaus interactions can potentially destroy Kondo singlet formation in such a system, and that the coupling to an electric field gives a mechanism to control transport properties. The most recent work focuses on correlations in interacting one-dimensional Bose gases. The asymptotic expression for correlation functions in a generalized Gibbs ensemble, where all the local conservation laws appear, is obtained from Bethe Ansatz and conformal field theory. In addition to the research papers with the above results, the thesis also contains an introductory text reviewing background material.
Parts of work
I. Erik Eriksson and Henrik Johannesson, Reduced fidelity in topological quantum phase transitions, Phys. Rev. A 79, 060301(R) (2009). ::doi::10.1103/PhysRevA.79.060301
 
II. Erik Eriksson and Henrik Johannesson, Corrections to scaling in entanglement entropy from boundary perturbations, J. Stat. Mech. (2011) P02008. ::doi::10.1088/1742-5468/2011/02/P02008
 
III. Erik Eriksson and Henrik Johannesson, Impurity entanglement entropy in Kondo systems from conformal field theory, Phys. Rev. B 84, 041107(R) (2011). ::doi::10.1103/PhysRevB.84.041107
 
IV. Erik Eriksson, Anders Ström, Girish Sharma, and Henrik Johannesson, Electrical control of the Kondo effect in a helical edge liquid, Phys. Rev. B 86, 161103(R) (2012). ::doi::10.1103/PhysRevB.86.161103
 
V. Erik Eriksson, Spin-orbit interactions in a helical Luttinger liquid with a Kondo impurity, arXiv:1303.3558.
 
VI. Erik Eriksson and Vladimir Korepin, Finite-size effects from higher conservation laws for the one-dimensional Bose gas, arXiv:1302.3182. (To appear in J. Phys. A: Math. Theor.)
 
Degree
Doctor of Philosophy
University
Göteborgs universitet. Naturvetenskapliga fakulteten
Institution
Department of Physics ; Institutionen för fysik
Disputation
Fredagen den 31 maj 2013, kl 13.15, Hörsal Euler, Skeppsgränd 3
Date of defence
2013-05-31
E-mail
erik.eriksson@physics.gu.se
URI
http://hdl.handle.net/2077/32678
Collections
  • Doctoral Theses / Doktorsavhandlingar Institutionen för fysik
  • Doctoral Theses from University of Gothenburg / Doktorsavhandlingar från Göteborgs universitet
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Avhandling (3.358Mb)
Spikblad (71.69Kb)
Date
2013-05-08
Author
Eriksson, Erik
Publication type
Doctoral thesis
ISBN
978-91-628-8707-0
Language
eng
Metadata
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