Book contents
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 Introduction
- 2 The Hubbard model
- 3 The magnetic instability of the Fermi system
- 4 The renormalization group and scaling
- 5 One-dimensional quantum antiferromagnets
- 6 The Luttinger liquid
- 7 Sigma models and topological terms
- 8 Spin-liquid states
- 9 Gauge theory, dimer models, and topological phases
- 10 Chiral spin states and anyons
- 11 Anyon superconductivity
- 12 Topology and the quantum Hall effect
- 13 The fractional quantum Hall effect
- 14 Topological fluids
- 15 Physics at the edge
- 16 Topological insulators
- 17 Quantum entanglement
- References
- Index
11 - Anyon superconductivity
Published online by Cambridge University Press: 05 March 2013
- Frontmatter
- Contents
- Preface to the second edition
- Preface to the first edition
- 1 Introduction
- 2 The Hubbard model
- 3 The magnetic instability of the Fermi system
- 4 The renormalization group and scaling
- 5 One-dimensional quantum antiferromagnets
- 6 The Luttinger liquid
- 7 Sigma models and topological terms
- 8 Spin-liquid states
- 9 Gauge theory, dimer models, and topological phases
- 10 Chiral spin states and anyons
- 11 Anyon superconductivity
- 12 Topology and the quantum Hall effect
- 13 The fractional quantum Hall effect
- 14 Topological fluids
- 15 Physics at the edge
- 16 Topological insulators
- 17 Quantum entanglement
- References
- Index
Summary
Anyon superconductivity
In this chapter we will consider the problemof predicting the behavior of an assembly of particlesobeying fractional statistics. We have already considered the problem of the quantum mechanics of systems of anyons. However, we did not consider what new phenomena may arise if the system has a macroscopic number of anyons present. At the time of writing, the physical reality of this problem is still unclear. However, this is such a fascinating problem that we will discuss it despite the lack of firm experimental support for the model.
There are two different physical situations in which the problem of anyons at finite density is important. Halperin, (1984) observed that the quasiparticles of the Laughlin state for the FQHE obeyed fractional statistics (i.e. they are anyons). In Chapter 13 we will discuss Halperin’s theory. Furthermore, Halperin and Haldane suggested that, for filling fractions of a Landau level different from the 1/m Laughlin sequence, the ground state of a 2D electron gas in a strong magnetic field could be understood as a Laughlin state of anyons. Shortly afterwards, Arovas, Schrieffer, Wilczek, and Zee (Arovas et al., 1985) studied the high-temperature behavior of a gas of anyons and calculated the second virial coefficient.
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- Field Theories of Condensed Matter Physics , pp. 414 - 431Publisher: Cambridge University PressPrint publication year: 2013