Field Theoretic Aspects of Condensed Matter Physics: An Overview

Abstract

In this chapter I discuss the impact of concepts of Quantum Field Theory in modern Condensed Physics. Although the interplay between these two areas is certainly not new, the impact and mutual cross-fertilization has certainly grown enormously with time, and Quantum Field Theory has become a central conceptual tool in Condensed Matter Physics. In this chapter I cover how these ideas and tools have influenced our understanding of phase transitions, both classical and quantum, as well as topological phases of matter, and dualities.

arXiv commentRevised version to appear as a chapter in the Encyclopedia of Condensed Matter Physics 2e. 126 pages, including 380 references

References in corpus (122)

• The electronic properties of graphene
• Topological insulators and superconductors
• Fault-tolerant quantum computation by anyons
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators with Inversion Symmetry
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological invariants of time-reversal-invariant band structures
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Topological quantum chemistry
• "Deconfined" quantum critical points
• Renormalization Group Approach to Interacting Fermions
• Continuous Quantum Phase Transitions
• Electronic Liquid Crystal Phases of a Doped Mott Insulator
• Theory of Intertwined Orders in High Temperature Superconductors
• Topological orders and Edge excitations in FQH states
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• An Electronic Mach-Zehnder Interferometer
• Nematic Fermi Fluids in Condensed Matter Physics
• Symmetry Protected Topological phases of Quantum Matter
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Quantum Field Theory in the Large N Limit: a review
• Quantum Theory of a Nematic Fermi Fluid
• Fractional statistics in anyon collisions
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Fermion Path Integrals And Topological Phases
• Chern-Simons Theory with Vector Fermion Matter
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Is the Composite Fermion a Dirac Particle?
• Topological Order and Conformal Quantum Critical Points
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Exact Conductance through Point Contacts in the $\nu =1/3$ Fractional Quantum Hall Effect
• Enhancement of superconductivity near a nematic quantum critical point
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Are non-Fermi-liquids stable to Cooper pairing?
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level
• Simulation of topological field theories by quantum computers
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Low Energy Dynamics of the Spinon-Gauge System
• Evidence for an axionic charge density wave in the Weyl semimetal (TaSe4)2I
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Particle-Vortex Duality from 3d Bosonization
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Correlation Functions of Large N Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• Fractional Quantum Hall Effect of Composite Fermions
• Observation of neutral modes in the fractional quantum Hall regime
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Quantum Hall states as matrix Chern-Simons theory
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Intertwined vestigial order in quantum materials: nematicity and beyond
• The Fermion-Boson Mapping in Three Dimensional Quantum Field Theory
• Masses in graphene-like two-dimensional electronic systems: topological defects in order parameters and their fractional exchange statistics
• Bosonization and Fermion Liquids in Dimensions Greater Than One
• Dual Dirac liquid on the surface of the electron topological insulator
• Chern-Simons Currents and Chiral Fermions on the Lattice
• Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal
• Theory of the Fabry-Perot Quantum Hall Interferometer
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Exact non-equilibrium DC shot noise in Luttinger liquids and fractional quantum Hall devices
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Fusion rules and vortices in $p_x+i{p}_y$ superconductors
• Bosonization of the Low Energy Excitations of Fermi Liquids
• Chern Simons duality with a fundamental boson and fermion
• Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2
• Bosonization of Fermi liquids
• Band Representations and Topological Quantum Chemistry
• Response functions and Spectrum of Collective Excitations of Fractional Quantum Hall Effect Systems
• A dipole interpretation of the $\nu =1/2$ state
• Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid
• Probing Non-Abelian Statistics with QuasiParticle Interferometry
• Local Charge of the nu=5/2 Fractional Quantum Hall State
• Observation of Chiral Heat Transport in the Quantum Hall Regime
• Real Space Renormalization in Statistical Mechanics
• Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals
• Signatures of fractional statistics in noise experiments in quantum Hall fluids
• Bosonization as Duality
• Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Current Correlations from a Mesoscopic Anyon Collider
• Universal structure of the edge states of the fractional quantum Hall states
• Multidimensional Bosonization
• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
• Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level
• Inter-edge strong-to-weak scattering evolution at a constriction in the fractional quantum Hall regime
• Effective field theories for topological insulators by functional bosonization
• Revisiting the Hanbury Brown-Twiss set-up for fractional statistics
• `Local' Quantum Criticality at the Nematic Quantum Phase Transition
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Superconductivity from repulsive interactions in the two dimensional electron gas
• Anyonic interference and braiding phase in a Mach-Zehnder Interferometer
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Gifts from anomalies: Exact results for Landau phase transitions in metals
• Non-commutative Chern-Simons for the Quantum Hall System and Duality
• Non-commutative field theory and composite Fermi Liquids in some quantum Hall systems
• What do noise measurements reveal about fractional charge in FQH liquids?
• Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
• Andreev reflection of fractional quantum Hall quasiparticles
• Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions
• Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• Correlations and beam splitters for quantum Hall anyons
• Lowest Landau level theory of the bosonic Jain states
• Quasi-particle tunneling at a constriction in a fractional quantum Hall state
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• A composite particle construction of the Fibonacci fractional quantum Hall state

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