Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Condensed Matter Physics
- Part II Quantum Field Theory
- Part III Quantum Field Theory Approach to Condensed Matter Systems
- 13 Quantum Field Theory Methods in Condensed Matter
- 14 Metals, Fermi Liquids, Mott and Anderson Insulators
- 15 The Dynamics of Polarons
- 16 Polyacetylene
- 17 The Kondo Effect
- 18 Quantum Magnets in 1D: Fermionization, Bosonization, Coulomb Gases and “All That”
- 19 Quantum Magnets in 2D: Nonlinear Sigma Model, CP1 and “All That”
- 20 The Spin-Fermion System: a Quantum Field Theory Approach
- 21 The Spin Glass
- 22 Quantum Field Theory Approach to Superfluidity
- 23 Quantum Field Theory Approach to Superconductivity
- 24 The Cuprate High-Temperature Superconductors
- 25 The Pnictides: Iron-Based Superconductors
- 26 The Quantum Hall Effect
- 27 Graphene
- 28 Silicene and Transition Metal Dichalcogenides
- 29 Topological Insulators
- 30 Non-Abelian Statistics and Quantum Computation
- Further Reading
- References
- Index
20 - The Spin-Fermion System: a Quantum Field Theory Approach
from Part III - Quantum Field Theory Approach to Condensed Matter Systems
Published online by Cambridge University Press: 25 October 2017
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Condensed Matter Physics
- Part II Quantum Field Theory
- Part III Quantum Field Theory Approach to Condensed Matter Systems
- 13 Quantum Field Theory Methods in Condensed Matter
- 14 Metals, Fermi Liquids, Mott and Anderson Insulators
- 15 The Dynamics of Polarons
- 16 Polyacetylene
- 17 The Kondo Effect
- 18 Quantum Magnets in 1D: Fermionization, Bosonization, Coulomb Gases and “All That”
- 19 Quantum Magnets in 2D: Nonlinear Sigma Model, CP1 and “All That”
- 20 The Spin-Fermion System: a Quantum Field Theory Approach
- 21 The Spin Glass
- 22 Quantum Field Theory Approach to Superfluidity
- 23 Quantum Field Theory Approach to Superconductivity
- 24 The Cuprate High-Temperature Superconductors
- 25 The Pnictides: Iron-Based Superconductors
- 26 The Quantum Hall Effect
- 27 Graphene
- 28 Silicene and Transition Metal Dichalcogenides
- 29 Topological Insulators
- 30 Non-Abelian Statistics and Quantum Computation
- Further Reading
- References
- Index
Summary
We have seen in the previous chapter how the dynamics of a two-dimensional quantum magnetic system on a square lattice can be described in the framework of the CP1/nonlinear sigma model. It is quite appealing, not only from the standpoint of basic principles but also from the point of view of modelling real materials, to investigate the behavior of electrons in the presence of this magnetic background. From this perspective, it would be interesting to study, among other issues: what would be the effective electronic interactions generated by the magnetic background, how these would depend on the phase transitions undergone by the underlying magnetic system, according to the values of different control parameters; what would be the role of skyrmion topological defects on the physical properties of the associated electrons; and how would electron or hole doping affect this interplay.
On the other hand, from the experimental point of view, several advanced materials have been obtained recently, the phase diagram of which present a very rich set of phases displaying different types of order. These are typically superconducting, magnetic or charge orders. Among these materials, we find heavy fermions such as CeCoIn5, high-Tc cuprates such as La2−x SrxCuO4 and iron pnictides, such as Sr1−x Kx Fe2As2. The richness of phases observed in such materials suggests there could be an underlying interaction responsible for the observed output, depending on the values of internal as well as external control parameters such as coupling constants and temperature, respectively. The spin-fermion model [174] describes this kind of system. Here we develop a quantum field theory approach the spinfermion system and investigate the possible effective interactions that are induced among the electrons by the (AF) magnetically ordered substrate.
Itinerant Electrons and Ordered Localized Spins
The Hamiltonian
We envisage a system containing both localized and itinerant electrons, the former belonging to atomic orbitals fixed to the sites of a square lattice. These generate localized magnetic dipole moments, which interact with nearest neighbors according to the SO(3), AF Heisenberg model. The itinerant electrons, conversely, have their kinematics determined by a tight-binding Hamiltonian, containing a hopping between nearest neighbors.
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- Quantum Field Theory Approach to Condensed Matter Physics , pp. 338 - 343Publisher: Cambridge University PressPrint publication year: 2017