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It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both…
The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…
For open systems subjected to external magnetic fields, relations between the statistical cumulants of their fluctuating currents and their response coefficients are established at arbitrary orders in the deviations from equilibrium, as a…
We propose a unifying theory for both the integral and fractional quantum Hall regimes. This theory reconciles the Finkelstein approach to localization and interaction effects with the topological issues of an instanton vacuum and…
I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields…
Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on…
The model of Composite Fermions for describing interacting electrons in two dimensions in the presence of a magnetic field is described. In this model, charged Fermions are combined with an even number of magnetic flux quanta in such a way…
We show that model states of fractional quantum Hall fluids at all experimentally detected plateau can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation motivated from physical…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
We propose an operator generalization of the Li-Haldane conjecture regarding the entanglement Hamiltonian of a disk in a 2+1D chiral gapped groundstate. The logic applies to regions with sharp corners, from which we derive several universal…
We numerically investigate the link between the delocalization-localization transition and entanglement in a disordered long-range hopping model of spinless fermions by studying various static and dynamical quantities. This includes the…
Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite…
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…
The fractional quantum Hall effect, where plateaus in the Hall resistance at values of coexist with zeros in the longitudinal resistance, results from electron correlations in two dimensions under a strong magnetic field. Current flows…
We argue that a correlated fluid of electrons and holes can exhibit a fractional quantum Hall effect at zero magnetic field analogous to the Laughlin state at filling $1/m$. We introduce a variant of the Laughlin wavefunction for electrons…
Fractional quantum Hall (FQH) states are examples of symmetry-enriched topological states (SETs): in addition to the intrinsic topological order, which is robust to symmetry breaking, they possess symmetry-protected topological invariants,…
We study the quantum self-organization of interacting particles in one-dimensional(1D) many-body systems, modeled via Hubbard chains with short-range interactions between the particles. We show the emergence of 1D states with density-wave…
Entanglement measures constitute powerful tools in the quantitative description of quantum many-body systems out of equilibrium. We study entanglement in the current-carrying steady state of a paradigmatic one-dimensional model of…
The observation of the fractional quantum Hall (FQH) effect in 2D electron gases ushered in investigations of topological phases driven by strong electron correlations. Their remarkable features include fractionalized elementary…