Quantum Scaling in Many-Body Systems
An Approach to Quantum Phase Transitions

Focusing on experimental results, this updated edition approaches the problem of quantum phase transitions from a new and unifying perspective.

Mucio Continentino (Author)

9781107150256, Cambridge University Press

Hardback, published 17 April 2017

246 pages, 39 b/w illus. 2 tables
25.4 x 17.9 x 1.5 cm, 0.64 kg

'The book is instructive, rich, stimulating and easy to follow, providing physical insight to many quantum critical phenomena where traditional theory becomes insufficient. The author draws attention to the physical interpretation and significant implications of the mathematical results presented here. The material is aimed at advanced graduate students in condensed matter or early career researchers … The book is very attractive, readable, containing discussions, comments or explanatory figures whenever is necessary. The author combines easy-to-grasp physical intuitive concepts with relevant mathematical expressions and advanced calculations, allowing the text to flow easily, in a highly organised and unified manner.' Eric Howard, Contemporary Physics

Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.

Preface
1. Scaling theory of quantum critical phenomena
2. Landau and Gaussian theories
3. Real space renormalization group approach
4. Renormalisation group: the expansion
5. Quantum phase transitions
6. Heavy fermions
7. A microscopic model for heavy fermions
8. Metal and superuid-insulator transitions
9. Density-driven metal-insulator transitions
10. Mott transitions
11. The non-linear sigma model
12. Superconductor quantum critical points
13. Topological quantum phase transitions
14. Fluctuation-induced quantum phase transitions
15. Scaling theory of first order quantum phase transitions
Appendix 1. Green's functions
References
Index.

Subject Areas: Nanotechnology [TBN], Quantum physics [quantum mechanics & quantum field theory PHQ], Physics [PH]