Related papers: Gaussian free fields at the integer quantum Hall p…
Generalized multifractality characterizes scaling of eigenstate observables at Anderson-localization critical points. We explore generalized multifractality in 2D systems, with the main focus on the spin quantum Hall (SQH) transition in…
We prove that the connectivity of the level sets of a wide class of smooth centred planar Gaussian fields exhibits a phase transition at the zero level that is analogous to the phase transition in Bernoulli percolation. In addition to…
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…
This paper has its motivation in the study of the Fractional Quantum Hall Effect. We consider 2D quantum particles submitted to a strong perpendicular magnetic field, reducing admissible wave functions to those of the Lowest Landau Level.…
We introduce Gutzwiller-correlated wave functions for the variational investigation of general multi-band Hubbard models. We set up a diagrammatic formalism which allows us to evaluate analytically ground-state properties in the limit of…
We consider transport properties of disordered two-dimensional electron gases under high perpendicular magnetic field, focusing in particular on the peak longitudinal conductivity $\sigma_{xx}^\mathrm{peak}$ at the quantum Hall plateau…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
The transition from the quantum Hall state to the insulator is considered for non-interacting electrons in a two-dimensional disordered lattice model with perpendicular magnetic field. Using correlated random disorder potentials the…
A careful study of the supersymmetric version of Pruisken's nonlinear sigma model for the integer quantum Hall effect is presented. The lattice regularized model is cast in Hamiltonian form by taking the anisotropic limit and interpreting…
We establish a general criterion for the positivity of the variance of a chaotic component of local functionals of stationary vector-valued Gaussian fields. This criterion is formulated in terms of the spectral properties of the covariance…
We study the quantum-mechanical decay of a Schwarzschild-like black hole into almost-flat space and weak radiation at a very late time, evaluating quantum amplitudes (not just probabilities) for transitions from initial to final states. No…
We study the critical properties of the non-interacting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at…
This thesis explores Quantum Field Theory (QFT) on curved spacetimes using a geometric Hamiltonian approach to the Schr\"odinger-like representation. In particular it studies the theory of the scalar field described through its…
To describe charged particles interacting with the quantized electromagnetic field, we point out the differences of working in the so-called generalized and the true Coulomb gauges. We find an explicit gauge transformation between them for…
It is commonly assumed in the studies of the fractional quantum Hall effect that the physics of a fractional quantum Hall state, in particular the character of its excitations, is invariant under a continuous deformation of the Hamiltonian…
We consider the level-sets of continuous Gaussian fields on $\mathbb{R}^d$ above a certain level $-\ell\in \mathbb{R}$, which defines a percolation model as $\ell$ varies. We assume that the covariance kernel satisfies certain regularity,…
Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantum Hall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-space…
I review the effective field theory (EFT) description of gravitating compact objects. The focus is on kinematic regimes where gravity is perturbative, in particular the adiabatic inspiral phase relevant to gravitational wave detection. For…
The fractional quantum Hall effect has been considered as a puzzling quantum many-body phenomenon that has yet to be fully explained. The plateau width and excitation energy gap are particularly problematic. We report here that those two…
We study quantum criticality in the infinite range Transverse-Field Ising Model. We find subtle differences with respect to the well-known single-site mean-field theory, especially in terms of gap, entanglement and quantum criticality. The…