Lowest Landau Level Stress Tensor and Structure Factor of Trial Quantum Hall Wave Functions

Nguyen, Dung Xuan; Son, D.; Wu, Chaolun

doi:10.48550/arxiv.1411.3316

Cited by 13 publications

(23 citation statements)

References 27 publications

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“…We thank D. T. Son for sharing with us Ref. [60], which gives an alternative derivation of (70). The work was supported by NSF DMS-1206648, DMS-1156656, DMR-MRSEC 0820054, John Templeton Foundation and PVE grant from the CNPq-Brazil Science Without Boarders Program.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

2015

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We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.

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Section: Acknowledgmentsmentioning

confidence: 99%

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

2015

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“…The same conservation law was derived previously in Ref. [40] using a LLL field theory formalism. The connection of volume-preserving diffeomorphism and quantum Hall physics was also noticed in Refs.…”

Section: Connection To Quantum Hall Effectmentioning

confidence: 72%

Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

Du,

Mehta,

Nguyen

et al. 2021

Preprint

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We propose nonabelian higher-rank gauge theories in 2+1D and 3+1D. The gauge group is constructed from the volume-preserving diffeomorphisms of space. We show that the intriguing physics of the lowest Landau level (LLL) limit can be interpreted as the consequences of the symmetry. We derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term within our formalism. Using the gauge symmetry in 2+1D, we derive the LLL effective action of vortex crystal in rotating Bose gas as well as Wigner crystal of electron in applied magnetic field. We show that the non-linear sigma models of ferromagnet in 2+1D and 3+1D exhibit the higher-rank gauge symmetries that we introduce in this paper.We interpret the fractonic behavior of the excitations on the lowest Landau level and of skyrmions in ferromagnets as the consequence of the higher-rank gauge symmetry.

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“…In Ref. [24] it was proven that I + (ω) = 0 for the trial ground states of model Hamiltonians with contact interactions. While there is no argument that I + should be zero for more general Hamiltonians, numerically it was found that for Coulomb interaction I + is much smaller than I − for the Laughlin ν = 1/3 state [20].…”

Section: Regimementioning

confidence: 99%

“…First we write down formulas for the full stress tensor. For the model Hamiltonian, at the long wave length regime k ∼ 0, the full stress tensor is the same as T kin [24]. For the general case, one needs to take into account the potential-energy term in the Lagrangian.…”

Section: Appendix A: Detailed Derivation Of Raman Scattering Couplingmentioning

confidence: 99%

Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering

Nguyen,

Son

2021

Preprint

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Starting from the Luttinger model for the band structure of GaAs, we derive an effective theory that describes the coupling of the fractional quantum Hall (FQH) system with photons in resonant Raman scattering experiments. Our theory is applicable in the regime when the energy of the photons ω 0 is close to the energy gap E G , but |ω 0 − E G | is much larger than the energy scales of the quantum Hall problem.In the literature, it is often assumed that Raman scattering measures the dynamic structure factor S(ω, k) of the FQH. However, in this paper, we find that the light scattering spectrum measured in the experiments are proportional to the spectral densities of a pair of operators which we identified with the spin-2 components of the kinetic part of the stress tensor. In contrast with the dynamic structure factor, these spectral densities do not vanish in the long-wavelength limit k → 0. We show that Raman scattering with circularly polarized light can measure the spin of the magnetoroton excitation in the FQH system. We give an explicit expression for the kinetic stress tensor that works on any Landau level and which can be used for numerical calculations of the spectral densities that enter the Raman scattering amplitudes.We propose that Raman scattering provides a way to probe the bulk of the ν = 5/2 quantum Hall state to determine its nature.

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Lowest Landau Level Stress Tensor and Structure Factor of Trial Quantum Hall Wave Functions

Cited by 13 publications

References 27 publications

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry

Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering

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