Chern-Simons Currents and Chiral Fermions on the Lattice

Abstract

We compute the Chern-Simons current induced by Wilson fermions on a $d=2n+1$ dimensional lattice, making use of a topological interpretation of the momentum space fermion propagator as a map from the torus to the sphere, $T^d\to S^d$. These mappings are shown to fall in different homotopy classes depending on the value of $m/r$, where $m$ is the fermion mass and $r$ is the Wilson coupling. As a result, the induced Chern-Simons term changes discontinuously at $d+1$ different values for $m$, unlike in the continuum. This behavior is exactly what is required by the peculiar spectrum found for a recently proposed model of chiral lattice fermions as zeromodes bound to a domain wall.

10 pages (1 figure not included), uses harvmac, UCSD-PTH-92-28

References in corpus (3)

• A Method for Simulating Chiral Fermions on the Lattice
• Chiral Fermions and Anomalies on a Finite Lattice
• Critical Momenta of Lattice Chiral Fermions

Cited by in corpus (120)

• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Chiral Fermions from Lattice Boundaries
• A construction of lattice chiral gauge theories
• Axial symmetries in lattice QCD with Kaplan fermions
• Chiral Determinant as an Overlap of Two Vacua
• Chiral Fermions on the Lattice
• Topological quantum matter with cold atoms
• Axion Electrodynamics in Topological Materials
• Topological Order Parameters for Interacting Topological Insulators
• Fluctuation driven topological Hund insulators
• Topological responses from chiral anomaly in multi-Weyl semimetals
• From the adiabatic theorem of quantum mechanics to topological states of matter
• Fluctuation-induced Topological Quantum Phase Transitions in Quantum Spin Hall and Quantum Anomalous Hall Insulators
• Surface states and chiral symmetry on the lattice
• Chiral Fermions on the Lattice
• Momentum space metric, non-local operator, and topological insulators
• From Standard Model of particle physics to room-temperature superconductivity
• Exact Boson-Fermion Duality on a 3D Euclidean Lattice
• Spacetime as a topological insulator: Mechanism for the origin of the fermion generations
• Symmetry-protected topological phases in lattice gauge theories: topological QED${}_2$
• Chiral properties of domain-wall quarks in quenched QCD
• Four-Dimensional N=1 Supersymmetric Yang-Mills Theory on the Lattice without Fine-Tuning
• Elasticity tetrads, mixed axial-gravitational anomalies, and 3+1d quantum Hall effect
• Electric circuit simulations of $n$th-Chern insulators in $2n$-dimensional space and their non-Hermitian generalizations for arbitral $n$
• Investigation of the Domain Wall Fermion Approach to Chiral Gauge Theories on the Lattice
• Wigner transformation, momentum space topology, and anomalous transport
• Atiyah-Patodi-Singer index from the domain-wall fermion Dirac operator
• Domain Wall Fermions and the Eta Invariant
• Nonperturbative Regulator for Chiral Gauge Theories?
• Domain wall fermions in a waveguide: the phase diagram at large Yukawa coupling
• Lattice Formulation of the Standard Model
• Exact holographic mapping in free fermion systems
• ${\mathbb{Z}}_N$ gauge theories coupled to topological fermions: QED${}_2$ with a quantum-mechanical $\theta$ angle
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Notes on topological insulators
• Chiral Defect Fermions and the Layered Phase
• Fermion masses through four-fermion condensates
• Tetrads in solids: from elasticity theory to topological quantum Hall systems and Weyl fermions
• Probing topological superconductors with emergent gravity
• Robust topological order in fermionic ${\mathbb{Z}}_2$ gauge theories: from Aharonov-Bohm instability to soliton-induced deconfinement
• Chiral symmetry on the lattice
• 3d Abelian Dualities with Boundaries
• Lattice Chiral Fermions
• Four-dimensional semimetals with tensor monopoles: From surface states to topological responses
• Metallic phase of the quantum Hall effect in four-dimensional space
• Anomalies and chiral defect fermions
• Invariants of disordered semimetals via the spectral localizer
• Domain wall fermion and chiral gauge theories on the lattice with exact gauge invariance
• Axial anomaly with the overlap-Dirac operator in arbitrary dimensions
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Momentum space topological invariants for the 4D relativistic vacua with mass gap
• Perturbative analysis for Kaplan's lattice chiral fermions
• The relation between the waveguide and overlap implementations of Kaplan's domain wall fermions
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• A Chiral Solution to the Ginsparg-Wilson Equation
• Chiral gauged fermions on a lattice
• Standard Model as the topological material
• Topological invariant in terms of the Green functions for the Quantum Hall Effect in the presence of varying magnetic field
• Boundary central charge from bulk odd viscosity - chiral superfluids
• A further study of the possible scaling region of lattice chiral fermions
• Vacuum Polarization and Chiral Lattice Fermions
• Topological insulators and topological non-linear sigma models
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• A Lattice Formulation of Chiral Gauge Theories
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Soft topological objects in topological media
• Recent Developments of Domain-wall/Overlap Fermions for Lattice QCD
• Axion response in gapless systems
• Generalized unparticles, zeros of the Green function, and momentum space topology of the lattice model with overlap fermions
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Topological chiral currents in the Gross-Neveu model extension
• Fractional quantum Hall effect in a relativistic field theory
• Is the doubler of the electron an antiquark?
• Precise Wigner-Weyl calculus for lattice models
• Species Doubling and Chiral Lagrangians
• On the Large Mass Limit of the Continuum Theories in Kaplan's Formulation
• Axial U(1) current in Grabowska and Kaplan's formulation
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• Vortex fermion on the lattice
• Little flavor: A model of weak-scale flavor physics
• Scaling property of domain-wall QCD in perturbation theory
• Weak coupling expansion of a chiral gauge theory on a lattice in the overlap formulation
• Quantum Monte Carlo simulation of topological phase transitions
• Perturbative study for domain-wall fermions in 4+1 dimensions
• Surface modes and chiral symmetry (Wilson Fermions in a box)
• Index theorems, generalized Hall currents and topology for gapless defect fermions
• Chern insulator transitions with Wilson fermions on a hyperrectangular lattice
• Domain-wall fermions with $U(1)$ dynamical gauge fields
• Lattice perturbation theory in the overlap formulation for the Yukawa and gauge interactions
• TKNN formula for general Hamiltonian
• A-geometrical approach to Topological Insulators with defects
• Note on Green Function Formalism and Topological Invariants
• Lattice chiral symmetry with hopping interactions
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Geometric construction of classes in van Daele's K-theory
• Interacting Chern Insulator in Infinite Spatial Dimensions
• ${\mathbb{Z}}_2$~Green's function topology of Majorana wires
• Chiral zero modes on the domain-wall model in 4+1 dimensions
• Hall conductivity as topological invariant in phase space
• Effective field theory of topological insulator and the Foldy-Wouthuysen transformation
• Discrete Wigner-Weyl calculus for the finite lattice
• Chiral fermions on lattice axion strings
• Chiral gauge theories with domain wall fermions
• Field Theoretic Aspects of Condensed Matter Physics: An Overview
• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• Decoupling of Layers in the Three-dimensional Abelian Higgs Model
• Eigenvalue crossings in Floquet topological systems
• Multilayer Haldane model
• The Effective field theory of 2+1 dimensional topological insulator in the presence of Rashba spin-orbit interaction
• Chiral symmetry on a lattice with hopping interactions
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation
• Species doubling and effective Lagrangians
• Topological invariant of multilayer Haldane models with irregular stackings