Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Part I Introduction
- Part II Quantum Ising and Rotor Models
- Part III Other Models
- 10 Boson Hubbard Model
- 11 Dilute Fermi and Bose Gases
- 12 Phase Transitions of Fermi Liquids
- 13 Heisenberg Spins: Ferromagnets and Antiferromagnets
- 14 Spin Chains: Bosonization
- 15 Magnetic Ordering Transitions of Disordered Systems
- 16 Quantum Spin Glasses
- References
- Index
12 - Phase Transitions of Fermi Liquids
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- Part I Introduction
- Part II Quantum Ising and Rotor Models
- Part III Other Models
- 10 Boson Hubbard Model
- 11 Dilute Fermi and Bose Gases
- 12 Phase Transitions of Fermi Liquids
- 13 Heisenberg Spins: Ferromagnets and Antiferromagnets
- 14 Spin Chains: Bosonization
- 15 Magnetic Ordering Transitions of Disordered Systems
- 16 Quantum Spin Glasses
- References
- Index
Summary
We will take the low-T Fermi liquid state of Section 11.2.2 in dimensions d ≥ 2 (or its spinful generalization) and examine the nature of its instabilities to other ground states of a dense gas of fermions. Possibilities include ferromagnets, states in which there is spin or charge density wave order (to be defined more precisely below), or various types of superconductors. All of these cases are of considerable practical importance and have numerous experimental applications.
A theoretical treatment of the quantum transition between a Fermi liquid and a magnetically or charge ordered state was given in a paper by Hertz, although many important points were anticipated in earlier work. We shall present Hertz's basic arguments in Section 12.1 for the case of a transition between a Fermi liquid and a spin density wave state. We shall not treat the other cases here and will, instead, refer the reader to the literature. There are a number of reasons for this neglect:
(i) Many aspects of these transitions are not fully understood (we will note some below) and are the subject of considerable debate in the literature; it is therefore inappropriate to include them in this introductory treatment.
(ii) We shall only consider systems in spatial dimensions d ≥ 2 here (the d = 1 case requires a separate treatment appropriate to Tomonaga–Luttinger liquids and will be addressed in Chapter 14).
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- Quantum Phase Transitions , pp. 229 - 239Publisher: Cambridge University PressPrint publication year: 2000