Related papers: Fuzzy spaces, the M(atrix) model and the quantum H…
We propose a finite Chern-Simons matrix model on the plane as an effective description of fractional quantum Hall fluids of finite extent. The quantization of the inverse filling fraction and of the quasiparticle number is shown to arise…
We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite…
A Gaussian approximation to the bosonic part of M-(atrix) theory with mass deformation is considered at large values of the dimension $d$. From the perspective of the gauge/gravity duality this action reproduces with great accuracy the…
We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…
A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These…
We reanalyse theoretical considerations and experimental data, in an attempt to decide hether there is another scale in the fractional quantum Hall effect problem, in addition to the magnetic scale defined by the magnetic length $a_c$ or…
The Quantum Hall Effects offer a rich variety of theoretical and experimental advances. They provide interesting insights on such topics as complementarity, gauge invariance, strong interactions, emergence of new theoretical concepts. This…
We report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field…
The quantum Hall effect is studied by introducing two different matrix variables for electrons and holes, having Chern-Simons type interactions. By generalizing the constraint condition proposed by Susskind to realize the Pauli's exclusion…
Following recent work on the quantum Hall effect on $S^4$, we solve the Landau problem on the complex projective spaces ${\bf C}P^k$ and discuss quantum Hall states for such spaces. Unlike the case of $S^4$, a finite spatial density can be…
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to…
The fluctuations in the spacing of the tunneling resonances through a quantum dot have been studied in the quantum Hall regime. Using the fact that the ground-state of the system is described very well by the Laughlin wavefunction, we were…
We consider the effect of contact interaction in a prototypical quantum spin Hall system of pseudo-spin-1/2 particles. A strong effective magnetic field with opposite directions for the two spin states restricts two-dimensional particle…
In this paper we propose a model of the fractional quantum Hall effect within conventional one-dimensional bosonization. It is shown that in this formalism the resulting bosonized fermion operator corresponding to momenta of Landau gauge…
The fractional quantum Hall effect (FQHE) is theoretically investigated, with numerical and algebraic approaches, in assemblies of a few spinful ultracold neutral fermionic atoms, interacting via repulsive contact potentials and confined in…
Making use of refermionization techniques, we map the nonlinear chiral Luttinger liquid model of the edge modes of a spatially confined fractional quantum Hall cloud developed in our recent work [Phys. Rev. A 107, 033320 (2023)] onto a…
Rotationally invariant fractional quantum Hall (FQH) states have long been understood in terms of composite bosons or composite fermions. Recent investigations of both incompressible and compressible states in highly tilted fields, which…
We derive the effective theories for quantum hall droplets with attractive interaction among the constituent particles. In the absence of confining potentials such droplets are defined by their freely moving interfaces (or boundaries) with…
Theoretical developments during the past several years have shown that large scale properties of the Quantum Hall system can be successfully described by effective field theories which use the Chern-Simons interaction. In this article, we…
This is a brief review on some properties of galaxies in the fuzzy dark matter model, where dark matter is an ultra-light scalar particle with mass $m = O(10^{-22})eV$. From quantum pressure, dark matter has a halo length scale which can…