Quantum Field Theory Approach to Condensed Matter Physics, Marino E., 2017

Quantum Field Theory Approach to Condensed Matter Physics, Marino E., 2017.

   A balanced combination of introductory and advanced topics provides a new and unique perspective on the quantum field theory (QFT) approach to condensed matter physics (CMP). Beginning with the basics of these subjects, such as static and vibrating lattices, independent and interacting electrons, the functional formulation for fields, different generating functionals and their roles, this book presents a unified viewpoint illustrating the connections and relationships among various physical concepts and mechanisms. Advanced and newer topics bring the book upto-date with current developments and include sections on cuprate and pnictide superconductors, graphene, Weyl semimetals, transition metal dichalcogenides, topological insulators and quantum computation. Finally, well-known subjects such as the quantum Hall effect, superconductivity, Mott and Anderson insulators, spin-glasses, and the Anderson-Higgs mechanism are examined within a unifying QFT-CMP approach. Presenting new insights on traditional topics, this text allows graduate students and researchers to master the proper theoretical tools required in a variety of condensed matter physics systems.




Independent Electrons in a Periodic Potential.
We will consider here the behavior of electrons in the presence of a periodic potential possessing the same symmetry as a given Bravais lattice. In this first approach we shall neglect the interactions of the electrons among themselves as well as the deviations from an ideal lattice, due, for instance, to thermal and quantum fluctuations. Such periodic potential is created by the basic constituents of the crystal, which are localized at each of the points of the crystalline structure. Its general form is given by (1.25).

The consequences of the presence of a periodic potential in a crystal are of foremost importance for the description of the electronic properties in a crystalline solid. Especially the kinematic properties of the electrons are profoundly modified, as well as the energy spectrum, charge and thermal conductivities, magnetic properties and so on.

Contents.
Part I Condensed Matter Physics.
1 Independent Electrons and Static Crystals.
2 Vibrating Crystals.
3 Interacting Electrons.
4 Interactions in Action.
Part II Quantum Field Theory.
5 Functional Formulation of Quantum Field Theory.
6 Quantum Fields in Action.
7 Symmetries: Explicit or Secret.
8 Classical Topological Excitations.
9 Quantum Topological Excitations.
10 Duality, Bosonization and Generalized Statistics.
11 Statistical Transmutation.
12 Pseudo Quantum Electrodynamics.
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.



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