APCTP Workshop: Field Theory and Geometry in Fractional Quantum Hall and Flat Band Systems

Contribution List

8. Welcome and Discussions

30/11/2025, 17:00

4. Probing quantum Hall systems through entanglement entropy and charge fluctuations

Benoit Estienne

01/12/2025, 09:40

Understanding how quantum information is distributed in many-body systems can reveal hidden structures and universal properties. In quantum Hall phases, the Li-Haldane conjecture provides a powerful guide: it proposes a bulk-edge correspondence for entanglement, asserting that the entanglement (or modular) Hamiltonian lies in the same universality class as the effective 1D Hamiltonian that...

10. Microscopic theory of geometric excitations in strongly-correlated topological Chern bands

Yuzhu Wang

01/12/2025, 10:40

We introduce a microscopic paradigm for geometric excitations called the graviton modes in Landau levels, and extend such studies to fractional Chern insulator (FCI) phases in moiré Chern bands. Strikingly, we identify an emergent guiding-center rotational symmetry in the FCI ground states and graviton modes, yet this symmetry is completely absent in the excitation continuum, leading to...

11. Emergent conformal Hilbert spaces and anyon dynamics in partially filled Chern bands

Bo Yang

01/12/2025, 12:00

The fractional quantum Hall (FQH) effect realized in Landau levels is a family of strongly correlated topological quantum fluids in two dimensional space, with exotic low-lying collective excitations that are anyonic and even non-Abelian. Here we propose a unified framework in understanding the integer and fractional quantum Hall systems via Hilbert spaces with emergent conformal symmetry, and...

12. Flat band and Kondo Physics in holographic mean field theory

Sang-Jin Sin

01/12/2025, 14:30

After introducing the hologhraphic mean field theory, I will talk about its application with flat band and Kondo physics in a strongly correlated material.

13. The Soliton Nature of the Super-Klein Tunneling Effect, Confinement, and Zero-Energy States in 2D Dirac Systems

Francisco Correa

01/12/2025, 15:30

This talk presents a unified view of soliton-induced transparency and supersymmetric confinement in two-dimensional Dirac systems. I first show how the super-Klein tunneling (SKT) effect arises from a correspondence between the Davey–Stewartson II (DS II) integrable system and quasi-exactly solvable Dirac Hamiltonians generated by DS II breather solutions. I then review supersymmetric methods...

14. Bloch electron on Moire superlattice: from superconductivity to non-coplanar spin systems

Moon Jip Park

02/12/2025, 10:00

Moiré superlattices in van der Waals heterostructures provide an exceptionally versatile platform in which electronic, orbital, and spin degrees of freedom can be engineered at the mesoscopic scale. By twisting or lattice-mismatching atomically thin layers, one can create flat or quasi-flat bands with strongly enhanced interaction effects, driving a rich assortment of correlated phases ranging...

15. Quantum Geometry for Fractional Chern Insulators and Exact Sum Rules

Jie Wang

02/12/2025, 11:00

Geometry is a fundamental mathematical concept that also plays a crucial role in characterizing the local properties of quantum states, including both pure and mixed states. Pure state geometry, often referred to as wavefunction geometry, is known to be important in many areas of zero-temperature condensed matter physics, such as the anomalous Hall effect and electron localization. Mixed state...

16. Ultra-Local Flat Bands, Carroll Symmetry, and Higher-Order Topology in 1D and 2D Fermion Models

Rudranil Basu

02/12/2025, 13:30

I will discuss a unified approach to constructing exactly flat bands in 1D and 2D lattice models using algebraic ultra-locality conditions equivalent to emergent Carroll symmetry. In 1D, this leads to compact localised states, commuting Hamiltonian densities, strictly local correlations, and subsystem-size independent entanglement entropy. Carroll-preserving interactions produce solvable...

17. Carroll at Phase Separation

Saikat Mondal

02/12/2025, 15:00

Recent years have witnessed growing interest in physical theories that go beyond the standard paradigm of Lorentz invariance, where Lorentz or Poincaré symmetry no longer governs the dynamics. This emerging direction, broadly referred to as non-Lorentzian physics, has proven to be a fertile ground for new insights across diverse areas such as condensed matter systems, hydrodynamics, and...

18. Carroll fermions

Lea Mele

02/12/2025, 15:50

Motivated by recent applications of Carroll symmetry, various Carroll-invariant field theories have been constructed and studied. Two distinct Carrollian theories, commonly referred to as magnetic and electric, can be obtained. In this talk, I will present the Carroll limits of relativistic spin-1/2 Dirac fermions in arbitrary spacetime dimensions. I will explain the subtlety that arise with...

19. Unconventional fractional Chern insulators in moiré systems

Raul Perea-Causin

03/12/2025, 09:30

I will review the recent progress on moiré fractional Chern insulators (FCIs), focusing on the recent predictions of non-Abelian phases, the experimental and theoretical work on Hall crystals, and the limitations of ideal quantum geometry as an indicator of FCIs. In this context, I will discuss the possibility of stabilizing Laughlin states in trivial bands, the potential emergence of...

20. Effective field theory for superfluid vortex crystals

Aleksander Glodkowski

03/12/2025, 10:20

Rotating Bose-Einstein condensates of trapped cold atoms form quantum vortex crystals. In this talk, I will present a bottom-up derivation of the effective field theory governing the low-energy excitations of such vortex crystals in two spatial dimensions. By embedding the system in Newton-Cartan geometry and analyzing the isometries of the resulting background, I identify the nonrelativistic...

21. Black Holes in Holography

Bum-Hoon Lee

04/12/2025, 10:00

We review various black holes in AdS space with the holographic point of view in mind. The topic to be included is the geometric realization of the phase transitions, the Maxwell construction, diverse phases in nonlinear charge interactions, etc. We also consider the ensemble dependence of the phases through the charged black holes, whose corresponding meaning in terms of the boundary field...

22. Magnetic defects and counting degrees of freedom

Matthew Roberts

04/12/2025, 11:00

Conformal field theories are wonderful universal objects that can be used to describe the deep infrared of strongly coupled systems, However, CFTs describe systems preserving all translations, rotations and boosts. If we consider systems with extended defects, in the deep infrared we find a more complicated system known as a defect CFT. These host an even richer structure than standard CFTs...

23. GMP algebra and fractonic dynamics of CP(N-1) skyrmions

Jung-Hoon Han

04/12/2025, 13:30

Skyrmions were proposed in 1961 by Tony Skyrme as a mathematical description of hadrons. Observation of the O(3) version of the skyrmion in two dimensions in a variety of magnetic materials since 2010 sparked keen interests in its structure, dynamics, and potential device applications. I give a brief review of the history of the theoretical and experimental progress in magnetic skyrmions over...

24. Flat bands: construction, properties and effects of perturbations

Alexei Andreanov

04/12/2025, 14:30

Flat bands are dispersionless energy bands in tight-binding networks.
The quenched kinetic energy (due to the absence of dispersion), makes them promising hosts for unconventional and exotic phases of matter in presence of perturbations, like disorder or interactions.
I will start with a overview of flat bands, and then discuss how flatbands can be constructed in various tight-binding...

25. Chiral Graviton Theory of Fractional Quantum Hall States

Yi-Hsien Du

05/12/2025, 10:00

Online talk - I will present a nonlinear, gauge-invariant effective field theory for the chiral graviton—the spin-2 neutral collective mode seen in polarized Raman scattering experiments on fractional quantum Hall states. The theory is constructed by gauging area-preserving diffeomorphisms with a unimodular spatial metric and introducing a Stueckelberg mass term that opens a tunable gap while...

26. Tkachenko mode in rotating superfluid and noncommutative field theory

Dam Thanh Son

05/12/2025, 11:00

Online talk - A superfluid rotates by creating a lattice of quantized vortices. The Tkachenko mode is an elastic wave propagating on the vortex lattice with two unusual properties: quadratic dispersion relation and absence of longitudinal polarization. We construct an effective field theory description of the Tkachenko mode using the formalism of noncommutative field theory. Using this theory...

9. Dinner

5. Opening

6. Registration

7. Registration