Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically massive Yang-Mills.
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Lectures on the Quantum Hall Effect
20 Pith papers cite this work. Polarity classification is still indexing.
20
Pith papers citing it
abstract
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective Chern-Simons theories, and the modes which live on the boundary. The notes are aimed at graduate students in any discipline where $\hbar=1$. A working knowledge of quantum field theory is assumed. Contents: 1. The Basics (Landau levels and Berry phase). 2. The Integer Quantum Hall Effect. 3. The Fractional Quantum Hall Effect. 4. Non-Abelian Quantum Hall States. 5. Chern-Simons Theories. 6. Edge Modes.
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hep-th 8 cond-mat.mes-hall 3 cond-mat.str-el 3 cond-mat.quant-gas 1 hep-ph 1 math.AP 1 math-ph 1 physics.optics 1 quant-ph 1roles
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background 4representative citing papers
Chern-Simons theory on a strip yields boundary current algebras for oppositely propagating chiral bosons whose velocities follow from a bulk-boundary consistency condition and are independent of strip width.
Under local spectral assumptions on the Bloch symbol h(k,X), H_ε admits L^{2}-normalized approximate eigenfunctions with residual O(ε^{m/2+1/4}) for m=1,2.
Compactification of the non-compact algebraic varieties of Z_N-graded Sugawara constructions on u(1)^2 Kac-Moody yields BMS3-like algebras Vir ⋊ F with F nilpotent of depth r < N for N>2, with depth tied to singularity order.
Quantum geometry in lattice compact scalar fields induces pair-dependent Chern couplings that produce non-identical anyons.
Flux quantization of the M5-brane tensor field in twisted Cohomotopy yields Pontrjagin homology observables that reproduce abelian Chern-Simons theory and braid actions on defect anyons.
Gauge transformations are shown to be the analog of W_infinity transformations for higher-dimensional quantum Hall effect, with their extended algebra and commutator anomaly derived via topological descent and bulk-boundary cancellation.
The replica-energy filter (1 − d^{-1} L ∂_L) on log Z isolates universal subextensive data in thermal QFT: central charges, sphere free energies, topological degeneracies, fracton degeneracies, and the Euler anomaly.
Derives order parameters and constructs the ground-state phase diagram for the interacting SSH model with extended hoppings, revealing multiple topological, SC-like, and CDW phases verified via large-system simulations.
The integer quantum Hall invariant N3 is expressed as a K-theory/cyclic-cohomology pairing; it vanishes on finite lattices and is only conditionally integer in the infinite-lattice limit.
Exact two-electron solutions in strong magnetic field organize into sub-Landau levels by relative angular momentum m, defining correlation subspaces that retain center-of-mass degeneracy and enable construction of pair-based many-body trial states.
Edge reconstruction of a ν=1 quantum Hall edge into a ν=1/3 side strip doubles topological sectors to Z2×Z2 degeneracy, producing 4π Josephson periodicity with energetically decoupled Z2 states.
Non-Hermitian Berry phases in time-varying media have a quantized real part due to symmetry, giving a topological index for systems including a non-Hermitian Su-Schrieffer-Heeger model.
Taub-NUT AdS black holes yield finite Hall transport coefficients originating from frame-dragging effects in holographic calculations.
An algorithm and analytic solutions are derived for Maxwell's equations with non-zero currents under Ohm's law, generalized Ohm's law with Hall effect, and added local fields, with an application to parallel waves.
Gauge symmetries of the Standard Model are suggested to be emergent, with an emergence scale of about 10^16 GeV making dark energy density similar in magnitude to light Majorana neutrino masses.
Spin term in particle current of pseudospin-1/2 BECs in synthetic gauge fields is required for classical drift velocity matching in non-interacting ground states and decreases relative to orbital current with increasing interactions.
Emergent Hall viscosity for integer quantum Hall phases in graphene is derived as a sum of geometric and electronic terms that depends on two topological invariants obtained via Green function Wigner-Weyl calculus.
A survey of ideal Bloch bands saturating quantum geometric bounds and their link to the lowest Landau level for fractionalized phases.
Lectures summarizing the construction of hydrodynamic EFTs through strong-to-weak symmetry breaking, with examples from spin chains to relativistic QFTs and UV/IR constraints on transport coefficients.
citing papers explorer
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Structure of Chern-Simons Graviton Scattering Amplitudes from Topological Graviton Equivalence Theorem and Double Copy
Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically massive Yang-Mills.
-
Edge modes in Chern-Simons theory on a strip
Chern-Simons theory on a strip yields boundary current algebras for oppositely propagating chiral bosons whose velocities follow from a bulk-boundary consistency condition and are independent of strip width.
-
Approximate eigenfunctions for some aperiodic crystals
Under local spectral assumptions on the Bloch symbol h(k,X), H_ε admits L^{2}-normalized approximate eigenfunctions with residual O(ε^{m/2+1/4}) for m=1,2.
-
$BMS_3$-like algebras via the $Z_N$-graded $u(1)^2$ Kac-Moody algebra
Compactification of the non-compact algebraic varieties of Z_N-graded Sugawara constructions on u(1)^2 Kac-Moody yields BMS3-like algebras Vir ⋊ F with F nilpotent of depth r < N for N>2, with depth tied to singularity order.
-
Non-identical anyon algebras from compact-field quantum geometry
Quantum geometry in lattice compact scalar fields induces pair-dependent Chern couplings that produce non-identical anyons.
-
Engineering of Anyons on M5-Probes via Flux Quantization
Flux quantization of the M5-brane tensor field in twisted Cohomotopy yields Pontrjagin homology observables that reproduce abelian Chern-Simons theory and braid actions on defect anyons.
-
Higher dimensional quantum Hall effect and the analog of $W_\infty$-algebra
Gauge transformations are shown to be the analog of W_infinity transformations for higher-dimensional quantum Hall effect, with their extended algebra and commutator anomaly derived via topological descent and bulk-boundary cancellation.
-
Nonadditivity in Quantum Field Theory: Replica Energies, Scaling Filters, and the Renormalization Group
The replica-energy filter (1 − d^{-1} L ∂_L) on log Z isolates universal subextensive data in thermal QFT: central charges, sphere free energies, topological degeneracies, fracton degeneracies, and the Euler anomaly.
-
Order parameters and ground-state phase diagram of the interacting topological Su-Schrieffer-Heeger model with extended-range hoppings
Derives order parameters and constructs the ground-state phase diagram for the interacting SSH model with extended hoppings, revealing multiple topological, SC-like, and CDW phases verified via large-system simulations.
-
Topological invariant responsible for the integer QHE and non-commutative geometry
The integer quantum Hall invariant N3 is expressed as a K-theory/cyclic-cohomology pairing; it vanishes on finite lattices and is only conditionally integer in the infinite-lattice limit.
-
Sub-Landau levels in two-dimensional electron system in magnetic field
Exact two-electron solutions in strong magnetic field organize into sub-Landau levels by relative angular momentum m, defining correlation subspaces that retain center-of-mass degeneracy and enable construction of pair-based many-body trial states.
-
Can Majorana zero modes in quantum Hall edges survive edge reconstruction?
Edge reconstruction of a ν=1 quantum Hall edge into a ν=1/3 side strip doubles topological sectors to Z2×Z2 degeneracy, producing 4π Josephson periodicity with energetically decoupled Z2 states.
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Partial Quantisation of Non-Hermitian Berry Phases in Time-Varying Media
Non-Hermitian Berry phases in time-varying media have a quantized real part due to symmetry, giving a topological index for systems including a non-Hermitian Su-Schrieffer-Heeger model.
-
Hall transports from Taub-NUT AdS black holes
Taub-NUT AdS black holes yield finite Hall transport coefficients originating from frame-dragging effects in holographic calculations.
-
On analytic solution of the Maxwell's equation with non-zero currents
An algorithm and analytic solutions are derived for Maxwell's equations with non-zero currents under Ohm's law, generalized Ohm's law with Hall effect, and added local fields, with an application to parallel waves.
-
Emergent Gauge Symmetries in Particle Physics and Cosmology
Gauge symmetries of the Standard Model are suggested to be emergent, with an emergence scale of about 10^16 GeV making dark energy density similar in magnitude to light Majorana neutrino masses.
-
Spin effects in the particle current of Bose-Einstein condensates in synthetic gauge fields
Spin term in particle current of pseudospin-1/2 BECs in synthetic gauge fields is required for classical drift velocity matching in non-interacting ground states and decreases relative to orbital current with increasing interactions.
-
Emergent Hall viscosity in the integer quantum Hall phases of graphene-like systems
Emergent Hall viscosity for integer quantum Hall phases in graphene is derived as a sum of geometric and electronic terms that depends on two topological invariants obtained via Green function Wigner-Weyl calculus.
-
Ideal Quantum Geometry for Fractional Chern Insulators
A survey of ideal Bloch bands saturating quantum geometric bounds and their link to the lowest Landau level for fractionalized phases.
-
Boulder Lectures on Thermal Dynamics and Hydrodynamic EFTs
Lectures summarizing the construction of hydrodynamic EFTs through strong-to-weak symmetry breaking, with examples from spin chains to relativistic QFTs and UV/IR constraints on transport coefficients.