Quantum Scaling in Many-Body Systems

An Approach to Quantum Phase Transitions

Mucio Continentino

• Publisher: Cambridge University Press
• Year: 2017
• ISBN:
  9781108184656
• Edition: 2
• Topic: Physical Sciences
• Subtopic: Physics
• Index: 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.

Table of contents

• Cover
• Half-title page
• Title page
• Copyright page
• Dedication page
• Contents
• Preface
• 1 Scaling Theory of Quantum Critical Phenomena
• 2 Landau and Gaussian Theories
• 3 Real Space Renormalisation Group Approach
• 4 Renormalisation Group: the ϵ-Expansion
• 5 Quantum Phase Transitions
• 6 Heavy Fermions
• 7 A Microscopic Model for Heavy Fermions
• 8 Metal and Superfluid–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
• References
• Index