We solve models of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> species of fermions in the lowest Landau level with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math>-invariant interactions in the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi><mo>≫</mo><mn>1</mn></mrow></math> limit. We find saddles of the second quantized path integral at fixed chemical potential corresponding to fractional Hall states with filling <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mi>p</mi><mo>/</mo><mi>q</mi><mo stretchy="false">)</mo></mrow></math>, where the integers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math> depend on the chemical potential and interactions. On a long torus there are <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi></math> such states related by translation symmetry, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>SU</mi><mo stretchy="false">(</mo><mi>N</mi><mo stretchy="false">)</mo></mrow></math>-invariant excitations of fractional charge. Remarkably, these saddles and their filling persist as extrema of the second-quantized action at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>=</mo><mn>1</mn></math>. Our construction gives a first-principles derivation of fractional Hall states from strongly interacting fermions.

Canada

Kristan Jensen

United States

Amir Raz

Fractional Hall Physics from Large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> Interacting Fermions

There exist metastable domain walls of the flavor-singlet meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>η</mi></mrow></math> for the U(1) axial symmetry in two-flavor color superconductivity (2SC) in quantum chromodynamics (QCD) at large baryon density. We show that, due to the coupling of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>η</mi></math> to confined SU(2) gluons in the 2SC phase, the effective theory on the domain wall is described by the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>SU</mi><mo stretchy="false">(</mo><mn>2</mn><msub><mo stretchy="false">)</mo><mrow><mo>−</mo><mn>1</mn></mrow></msub></math> Chern-Simons theory, which is dual to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mn>2</mn></msub></math> Chern-Simons theory. This theory has a spin-1 droplet excitation that does not carry a baryon number, which we identify as a vector meson. We also discuss the effective theories and baryonic droplet excitations on the domain walls of the flavor-singlet mesons in the superfluid phases of QCD at large isospin density and two-color QCD at large baryon density.

Japan

Kentaro Nishimura

Naoki Yamamoto

Ryo Yokokura

Quantum Hall liquids in high-density QCD

How to understand the integral and fractional quantum Hall resistivity in an unified mathematical physics theory remained an unsolved problem in the past four decades. Here the quantum Hall fluid is modeled as electron fluid membrane that winds around magnetic fluxes. The train tracks of fractional quantum Hall fluid lies in the cross section edge surface of the folded membrane, which is spontaneously characterized by the knot lattice of magnetic fluxes in the bulk zone. The transition from the fractional Hall fluid to the integral Hall fluid is characterized by a geometric transformation in hyperbolic space. Both the integral and fractional Hall resistivity are unified into one exact resistivity equation, <math altimg='si1.svg'><msub><mrow><mi>R</mi></mrow><mrow><mi>x</mi><mi>y</mi></mrow></msub><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mo stretchy='false'>(</mo><mi>h</mi><mo stretchy='false'>/</mo><msup><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy='false'>)</mo><mi>B</mi><mo stretchy='false'>(</mo><mi>m</mi><mo stretchy='false'>)</mo></math>, <math altimg='si2.svg'><mi>B</mi><mo stretchy='false'>(</mo><mi>m</mi><mo stretchy='false'>)</mo><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><msup><mrow><mo stretchy='false'>(</mo><mi>n</mi><mo linebreak='badbreak' linebreakstyle='after'>+</mo><mi>&#957;</mi><mo stretchy='false'>(</mo><mi>m</mi><mo stretchy='false'>)</mo><mo stretchy='false'>)</mo></mrow><mrow><mo linebreak='badbreak' linebreakstyle='after'>&#8722;</mo><mn>1</mn></mrow></msup></math>, with respect to the bulk energy gap <math altimg='si3.svg'><mi mathvariant='normal'>&#916;</mi><mi>E</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mi>&#295;</mi><mi>e</mi><mi>B</mi><mo stretchy='false'>(</mo><mi>m</mi><mo stretchy='false'>)</mo><mo stretchy='false'>/</mo><mi>M</mi><mi>c</mi></math>, that agrees with experimental measurements. This electron fluid membrane model provides a natural representation of Wen-Zee matrix formulation of topological fluid for quantum Hall effect under topological surgery and train track. When the electron fluid membrane in real space is mapped into momentum space, the Thouless-Kohmoto-Nightingale-Den Nijs (TKNN) formula of integral Hall conductance is generalized to fractional Hall conductance. The Thurston's train track in two dimensions is generalized to the folding laminar membranes in three dimensions, which predicted fractional quantum Hall fluid in three dimensions, and provided an analytical explanation on the measured competing phenomena between different fractional quantum Hall states. A fractional quantum Hall effect in hyperbolic space is predicted in the plane perpendicular to the conventional 2D electron gas in inhomogeneous magnetic field. This topological representation theory provides a different path to implement string theory and topological quantum computation by folding laminar quantum fluid.

China

Tieyan Si

An unified topological representation theory of the integral and fractional quantum Hall fluid by folding the membrane of quantum electron fluid

The particle with first-order dynamics proposed by Dunne, Jackiw, and Trugenberger (DJT) to justify the Peierls substitution is obtained by reduction from both of the planar two-parameter centrally extended Galilean and Carroll systems. In the latter case the extension parameters <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mi>e</mi><mi>x</mi><mi>o</mi></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>κ</mi></mrow><mrow><mi>mag</mi></mrow></msub></mrow></math> generate noncommutativity of the coordinates resp. behave as an internal magnetic field. The position and momentum follow uncoupled anomalous Hall motions. Consistently with partial immobility, one of the Carroll boost generators is broken but the other remains a symmetry. Switching off <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>κ</mi><mrow><mi>e</mi><mi>x</mi><mi>o</mi></mrow></msub></math>, the immobility of unextended Carroll particles is recovered. The Carroll system is dual to an uncharged anyon on the horizon of a black hole which exhibits the spin-Hall effect. Physical applications are shortly reviewed.

H.X. Zeng

Q.L. Zhao

P.M. Zhang

France

P.A. Horvathy

Peierls substitution and Hall motion in exotic Carroll dynamics

Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the parton picture used in two spatial dimensions, the crucial ingredient being the cancellation of anomalies for the gauge fields binding the partons together. Some subtleties which exist even in two dimensions are pointed out. The effective action is obtained from a combination of the Dolbeault and Dirac index theorems. We also present expressions for some transport coefficients such as Hall conductivity and Hall viscosity for the fractional states.

Abhishek Agarwal

Dimitra Karabali

V. P. Nair

Fractional quantum Hall effect in higher dimensions

Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasi-particles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless “electric” field and a “magnetic” vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial “flux-attachment” relation for dipoles. This gives a possible starting point for a fracton-vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model.

Ireland

Erica Bertolini

Italy

Alberto Blasi

Nicola Maggiore

Daniel Shaikh

Hall-like behaviour of higher rank Chern-Simons theory of fractons

Vortex light, characterized by an intrinsic orbital angular momentum aligned with its propagation direction, is described through vortex electromagnetic waves. Similar to the gravitational spin Hall effect (SHE), vortex light is expected to exhibit intrinsic orbital angular momentum dependent trajectories and deviations from the null geodesic plane when propagating through a gravitational field, a phenomenon termed the gravitational orbital Hall effect (OHE). In this work, we model the vortex light as vortex Laguerre–Gaussian electromagnetic wave packets and analyze its motion by solving covariant Maxwell equations within the Lense–Thirring metric. Our findings reveal that the trajectory of vortex light with an intrinsic orbital angular momentum deviates from the null geodesic in two ways. It deviates both perpendicular to, and within, the null geodesic plane. This behavior contrasts with the gravitational SHE, where spin-polarized light primarily deviates perpendicular to the null geodesic plane. Moreover, the relationship between the deviation and intrinsic orbital angular momentum differs significantly from that between the deviation and spin. These results suggest a unique interaction between intrinsic orbital angular momentum and gravity, distinct from the spin-gravity coupling, indicating that the gravitational OHE of light might not be precisely predicted by merely substituting spin with intrinsic orbital angular momentum in the gravitational SHE of light.

Wei-Si Qiu

Dan-Dan Lian

Peng-Ming Zhang

Gravitational orbital Hall effect of vortex light in Lense–Thirring metric

We show that a system of particles on the lowest Landau level can be coupled to a probe U(1) gauge field <math> <mi>A</mi> </math> $$ \mathcal{A} $$ μ in such a way that the theory is invariant under a noncommutative U(1) gauge symmetry. While the temporal component <math> <mi>A</mi> </math> $$ \mathcal{A} $$ 0 of the probe field is coupled to the projected density operator, the spatial components <math> <mi>A</mi> </math> $$ \mathcal{A} $$ i are best interpreted as quantum displacements, which distort the interaction potential between the particles. We develop a Seiberg-Witten-type map from the noncommutative U(1) gauge symmetry to a simpler version, which we call “baby noncommutative” gauge symmetry, where the Moyal brackets are replaced by the Poisson brackets. The latter symmetry group is isomorphic to the group of volume preserving diffeomorphisms. By using this map, we resolve the apparent contradiction between the noncommutative gauge symmetry, on the one hand, and the particle-hole symmetry of the half-filled Landau level and the presence of the mixed Chern-Simons terms in the effective Lagrangian of the fractional quantum Hall states, on the other hand. We outline the general procedure which can be used to write down effective field theories which respect the noncommutative U(1) symmetry.

Yi-Hsien Du

Umang Mehta

Dam Son

Noncommutative gauge symmetry in the fractional quantum Hall effect

Abstract Plateau–plateau transition in the integer quantum Hall effect is a phase transition between metal and insulator. The behavior describing how the width ΔB of the transition changes with temperature and frequency of radiations imposed has been explored extensively. It decreases with the decrease of temperature and frequency, but saturates at a critical temperature or frequency. We have recently discussed the effect of axion dark matter on the saturation. The axion generates radiations under a strong magnetic field in the experiment of the quantum Hall effect. The radiations play a similar role to that of radiations imposed externally. In this paper we discuss in detail how the width behaves in relation to temperature and frequency under the effect of axion dark matter. We show that the axion effect can be observable in low temperatures roughly below 100 mK. According to our detailed analysis of the saturation, we find that the critical frequency of saturation observed in the previous experiment strongly suggests axion mass m$_{a}$ = (0.95∼0.99) × 10$^{−5}$ eV.

Aiichi Iwazaki

Axion Detection with Quantum Hall Effect The Rydberg-Atom-Cavity Axion Search

We systematically derive the chiral kinetic theory for chiral fermions with collisions, including the self-energy corrections, from quantum field theories. We find that the Wigner functions and chiral kinetic equations receive both the classical and quantum corrections from the self-energies and their spacetime gradients. We also apply this formalism to study nonequilibrium neutrino transport due to the interaction with thermalized electrons and nucleons, as realized in core-collapse supernovae. We derive neutrino currents along magnetic fields and neutrino spin Hall effect induced by the density gradient at first order in the Fermi constant <math><msub><mi>G</mi><mi>F</mi></msub></math> for anisotropic neutrino distributions.

Taiwan

Di-Lun Yang

Chiral kinetic theory with self-energy corrections and neutrino spin Hall effect