Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Scaling Theory of Quantum Critical Phenomena
- 2 Landau and Gaussian Theories
- 3 Real Space Renormalisation Group Approach
- 4 Renormalisation Group: the ∊-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
14 - Fluctuation-Induced Quantum Phase Transitions
Published online by Cambridge University Press: 04 May 2017
- Frontmatter
- Dedication
- Contents
- Preface
- 1 Scaling Theory of Quantum Critical Phenomena
- 2 Landau and Gaussian Theories
- 3 Real Space Renormalisation Group Approach
- 4 Renormalisation Group: the ∊-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
Summary
Introduction
The quantum phase transitions considered so far in this book are mostly continuous, second order. They are associated with the divergence of a correlation length and of a characteristic time that renders the quantum critical point scale invariant. However, there are many important phase transitions at which the order parameter goes abruptly to zero and, more important, at which the characteristics of length and critical time do not diverge. In general there is also a latent heat, or work required, to transform one phase into another. In this and the next chapter we study these discontinuous quantum phase transitions. We proceed by considering initially some important cases of what is known as fluctuation induced quantum phase transitions to next treat a more general case of a first-order quantum phase transition. We will show through the study of these problems that the concepts of critical exponents and scaling remain useful, even though these systems do not exhibit scale invariance at their critical point. In Chapter 15 we present the scaling theory of first-order quantum phase transitions and use its results to treat some general problems.
One of the most interesting cases of fluctuation-induced transitions occurs in superconductors due to the coupling of the charged carriers to the electromagnetic field. We consider initially a wider class of systems with macroscopic wave functions, the superfluids, of which superconductors are the charged version. We adopt a macroscopic approach to this problem and describe the superfluid by a complex order parameter φ, such that |φ|2 is proportional to the density of condensed particles. The zero temperature phase diagram is expressed in terms of a control parameter, m2, such that, at m2 = 0, the system presents a quantum phase transition from a superfluid state, for m2 < 0, φ ≠ 0, to a normal state for m2 > 0 where φ = 0. In the case of the superconductor with particles of charge q = 2e, we will include the coupling of these particles to the electromagnetic field and study its effect in the phase diagram of these systems. We show that in the neutral superfluid, the zero temperature transition to the normal state is continuous and occurs at a quantum critical point.
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- Quantum Scaling in Many-Body SystemsAn Approach to Quantum Phase Transitions, pp. 196 - 216Publisher: Cambridge University PressPrint publication year: 2017