Field Theories of Condensed Matter Physics

  title={Field Theories of Condensed Matter Physics},
  author={Eduardo Fradkin},
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 quantum Hall effect 13. The fractional quantum Hall effect 14. Topological fluids 15. Physics at the edge 16… 
Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
The interplay between symmetry and topology is one of the most exciting avenues of modern condensed matter research. Here, the authors propose a new and unified approach for describing the low-energy
Topology, geometry and quantum interference in condensed matter physics
The methods of quantum field theory are widely used in condensed matter physics. In particular, the concept of an effective action was proven useful when studying low temperature and long distance
Confined Phases of One-Dimensional Spinless Fermions Coupled to Z_{2} Gauge Theory.
This work investigates a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field and develops an exactly solvable effective theory of bosonic dimers with emergent constraints at strong coupling.
Physics ) TITLE : A model for a Fractionalized Quantum Spin Hall Effect
Effects of electron correlations on a two dimensional quantum spin Hall system are studied. We examine possible phases of a generalized Hubbard model on a bilayer honeycomb lattice with a spin-orbit
Renormalization group study of interaction-driven quantum anomalous Hall and quantum spin Hall phases in quadratic band crossing systems
It is shown that topological insulating phases driven by interactions can be realized without the need for spin-orbit coupling or large intersite interaction in a two-dimensional system of spin-1/2
A short guide to topological terms in the effective theories of condensed matter
This article takes up several prominent examples, mainly from the area of quantum magnetism and superfluids/superconductors, and briefly discusses how these ideas are now finding incarnations in the studies of symmetry-protected topological phases.
Three-dimensional topological insulators and bosonization
A bstractMassless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and
A Study of Asymptotic Freedom for Topological Insulator
We study and present the results of quantum Berezinskii-Kosterlitz-Thouless (BKT) transition for interacting helical liquid system at the edge of topological insulator. We present results for
On the Dynamics of Phase Transitions in Relativistic Scalar Field Theory
Abstract We study the Kibble–Zurek scaling dynamics and universal second order phase transitions in a relativistic scalar field theory in 1 + 1 dimensions. Using tensor networks techniques as a
Exact solutions of topological superconductor model with Hubbard interactions
Abstract We study a two-dimensional model of topological superconductor with equal spin pairing and repulsive Hubbard interaction. When the pairing gap equals to the hopping constant, half of the


The One-Dimensional Hubbard Model
Preface 1. Introduction 2. The Hubbard Hamiltonian and its symmetries 3. The Bethe ansatz solution 4. String hypothesis 5. Thermodynamics in the Yang-Yang approach 6. Ground state properties in the
Chern-Simons gauge theories, confinement, and the chiral spin liquid.
It is shown that, as a result of the lack of gauge invariance of the determinant of the Dirac operator with a monopole background, the monopoles do not contribute to the Euclidean path integral, that fermions carrying the fundamental charge are not confined and that the spectrum of chiral-spin-liquid phases of theories of high-temperature superconductors supports separation of spin and charge.
Mean-field theory of spin-liquid states with finite energy gap and topological orders.
  • Wen
  • Physics, Medicine
    Physical review. B, Condensed matter
  • 1991
The mean-field theory of a T- and P-symmetric spin-liquid state is developed. The quasiparticle excitations in the spin-liquid state are shown to be spin-1/2 neutral fermions (the spinons) and charge
Quantum Impurity Problems in Condensed Matter Physics
Impurities are ubiquitous in condensed matter. Boundary Conformal Field Theory (BCFT) provides a powerful method to study a localized quantum impurity interacting with a gapless continuum of
Correlation effects in quantum spin-Hall insulators: a quantum Monte Carlo study.
In the quantum spin-Hall state the Kane-Mele model supplemented by a Hubbard U term is considered, and the spin, charge, and single-particle dynamics of the helical Luttinger liquid is studied by retaining the Hubbard interaction only on a ribbon edge.
Solitons with Fermion Number 1/2 in Condensed Matter and Relativistic Field Theories
States with fractional fermion charge have been discovered in relativistic field theory and condensed matter physics. In the latter context they lead to unexpected but experimentally verified
Non-Fermi liquid fixed point in 2 + 1 dimensions
Abstract We construct models of excitations about a Fermi surface that display calculable deviations from Fermi liquid behavior in the low-energy limit. They arise as a consequence of coupling to a
Time-reversal symmetric hierarchy of fractional incompressible liquids
We provide an effective description of fractional topological insulators that include the fractional quantum spin Hall effect by considering the time-reversal symmetric pendant to the topological
Topological BF field theory description of topological insulators
Research Highlights: > We show that a BF theory is the effective theory of 2D and 3D topological insulators. > The non-gauge-invariance of the bulk theory yields surface terms for a bosonized Dirac
Principles of condensed matter physics
Preface 1. Overview 2. Structure and scattering 3. Thermodynamics and statistical mechanics 4. Mean-field theory 5. Field theories, critical phenomena, and the renormalization group 6. Generalized