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An effective wavefunction for the edge excitations in the Fractional quantum Hall effect can be found by dimensionally reducing the bulk wavefunction. Treated this way the Laughlin $\nu=1/(2n+1)$ wavefunction yields a Luttinger model ground…
We consider two heteronuclear atoms interacting with a short-range $\delta$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical…
Starting from a microscopic description of a system of strongly interacting electrons in a strong magnetic field in a finite geometry, we construct the boundary low energy effective theory for a fractional quantum Hall droplet taking into…
Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature.…
One dimensional conductors are described by Luttinger liquid theory, which predicts a power-law suppression of the density of states near the Fermi level. The scaling exponent is non-universal in the general case, but is predicted to be…
We use chiral Luttinger liquid theory to study transport through a quantum dot in the fractional quantum Hall effect regime and find rich non-Fermi-liquid tunneling characteristics. In particular, we predict a remarkable…
The spectrum and the eigenstates of a finite 2D tight-binding electronic system, with Dirichlet boundary conditions, in magnetic field and external linear potential are studied. The eigenstates show an equipotential character and may cross…
We show that one-dimensional quantum systems with gapless degrees of freedom and open boundary conditions form a new universality class of quantum critical behavior, which we propose to call ``bounded Luttinger liquids''. They share the…
We have developed a theory of quasiparticle backscattering in a system of point contacts formed between single-mode edges of several Fractional Quantum Hall Liquids (FQHLs) with in general different filling factors $\nu_j$ and one common…
Recent studies on confined crystals of charged colloidal particles are reviewed, both in equilibrium and out of equilibrium. We focus in particular on direct comparisons of experiments (light scattering and microscopy) with lattice sum…
We study the effect of electron-electron interaction on the charge and spin structures at the edge of integer quantum Hall liquids, under three different kinds of confining potentials. Our exact diagonalization calculation for small systems…
We identify the the ground-state of a truncated version of Haldane's pseudo-potential Hamiltonian in a thin cylinder geometry as being composed of exponentially many fragmented matrix product states. These states are constructed by lattice…
We consider the problem of an ideal polymer confined in a droplet. When the droplet radius is smaller than the (unconfined) polymer radius of gyration, the polymer entropy will depend on the droplet shape. We compute the resulting surface…
We consider electron transport through a quantum point contact between compressible Quantum Hall liquids and derive the contact's impedance function for both diffusive and ballistic regimes of the bulk electron motion. In either regime, the…
We use particle entanglement spectra to characterize bosonic quantum Hall states on lattices, motivated by recent studies of bosonic atoms on optical lattices. Unlike for the related problem of fractional Chern insulators, very good trial…
Recent breakthrough experiments have demonstrated how it is now possible to explore the dynamics of quantum Hall states interacting with quantum electromagnetic cavity fields. While the impact of strongly coupled non-local cavity modes on…
Lanthanide atoms have an unusual electron configuration, with a partially filled shell of $f$ orbitals. This leads to a set of characteristic properties that enable enhanced control over ultracold atoms and their interactions: large numbers…
The importance of quantum effects for exotic nuclear shapes is demonstrated. Based on the example of a sheet of nuclear matter of infinite lateral dimensions but finite thickness, it is shown that the quantization of states in momentum…
The combination of interactions and static gauge fields plays a pivotal role in our understanding of strongly-correlated quantum matter. Cold atomic gases endowed with a synthetic dimension are emerging as an ideal platform to…
Motivated by a recent Comment by J. H\"oller and N. Read [Phys. Rev. B 93, 197401 (2016)], we revisit the problem of a chiral Luttinger liquid on a boundary of a Galilean-invariant quantum Hall fluid. After correcting the linear response…