Quantum phase transitions in magnetic systems: application of coupled cluster method [Elektronische Ressource] / vorgelegt von Rachid Darradi

Sujets

• Physik

Informations

• Publié par: otto-von-guericke-universitat_magdeburg
• Publié le: 01 janvier 2009
• Nombre de lectures: 20
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Quantum phase transitions in magnetic systems:
Application of coupled cluster method
DISSERTATION
zur Erlangung des akademischen Grades
doctor rerum naturalium
(Dr. rer. nat. )
der Fakultat fur Naturwissenschaften
der Otto-von-Guericke-Universitat Magdeburg
vorgelegt von
Diplomphysiker Rachid Darradi
Magdeburg, 27. Oktober 2008Quantum phase transitions in magnetic systems:
Application of coupled cluster method
DISSERTATION
zur Erlangung des akademischen Grades
doctor rerum naturalium
(Dr. rer. nat. )
genehmigt durch die Fakultat fur Naturwissenschaften
der Otto-von-Guericke-Universitat Magdeburg
von Diplomphysiker Rachid Darradi
geboren am 25. November 1970
in Khouribga (Marokko)
Gutachter: Prof. Dr. Johannes Richter
PD Dr. Andreas Honecker
eingereicht am: 27.10.2008
verteidigt am: 26.01.2009Dedication
This work is dedicated to my family, who supported me with
their love, care and prayers.
iiiAcknowledgments
First of all, I would like to express my deepest gratitude to my supervisor, Profes-
sor Johannes Richter for providing me an opportunity to work with him on number
of interesting and challenging physical questions. His professional guidance, inspira-
tional help, constructive criticism, and continuous support helped me to nish my work
successfully. Really, without his guidance this work would not have been accomplished.
I would like to thank Dr. Damian Farnell and Dr. Sven Kruger for their timely help,
valuable discussions and encouragement. I am also highly indebted to the Rechen-
zentrum of the University Magdeburg and in particular to Dr. Jorg Schulenburg for
assistance in numerical calculations.
I am grateful to Professor Raymond Bishop for giving me the chance of an educa-
tional visit at the University of Manchester and due to this educational visit, I was
able to develop new ideas for my research work.
I would like to acknowledge the University of Magdeburg for nancial support and
Germany Research Foundation (Deutsche Forschungsgemeinschaft) for nancial sup-
port (No. Ri614/14-1, Ri615/12-1, and No. Ih13/7-1).
I would like to thank my colleagues Reimar Schmidt, Dr. Dirk Schmalfu , Ronald
Zinke and Moritz Hartel for their good cooperation, many stimulating co ee breaks,
and useful discussions. Special thanks to our secretary Silvia Simon for all her patience
with me.
Finally, I must give immense thanks to my parents, my sisters, my brothers, and
of course my wife and my children for their love, and moral support.
vContents
Dedication iii
Acknowledgments v
List of Figures xi
List of Tables xvii
1. Introduction 1
2. Many-Body Method: The coupled cluster method (CCM) 7
2.1. The CCM ground-state formalism . . . . . . . . . . . . . . . . . . . . . 7
2.2. The CCM for quantum spin lattices . . . . . . . . . . . . . . . . . . . . 9
2.2.1. Choice of CCM model state . . . . . . . . . . . . . . . . . . . . 9
2.2.2. Commutation relations and the high-order general-s CCM for-
malism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3. Hierarchical approximation schemes . . . . . . . . . . . . . . . . 11
2.2.4. The ket-state equations . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.5. The bra-state equations . . . . . . . . . . . . . . . . . . . . . . 14
2.3. The excited-state formalism . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4. Calculation of physical quantities using CCM . . . . . . . . . . . . . . 17
2.4.1. Ground state energy and Sublattice magnetization . . . . . . . . 17
2.4.2. Spin sti ness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4.3. Generalized susceptibilities . . . . . . . . . . . . . . . . . . . . . 18
2.5. Extrapolation Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.6. The CCM for the pure Heisenberg antiferromagnet on square
and cubic lattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3. Quantum phase transitions in 2D unfrustrated Heisenberg antiferro-
0magnet - J{J model 23
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2. The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3. Inuence of Ising-anisotropy . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.1. Variational mean- eld approach . . . . . . . . . . . . . . . . . . 25
3.3.2. Coupled cluster method . . . . . . . . . . . . . . . . . . . . . . 26
3.3.3. Exact diagonalization . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.4. Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
vii