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In this paper, we present a description of Haldane's Luttinger liquid which parallels Laughlin's theory of the Fractional Quantum Hall (FQH) incompressible fluid, both exhibiting similar ground states as well as fractional excitations.…

The density-density correlation functions (most singular parts) of chiral Luttinger liquids forming the fractional quantum Hall effect (FQHE) edge are systematically derived in presence of a point-contact junction acting as a localised…

Haldane hypothesis about the universality of Luttinger liquid (LL) behavior in conducting one-dimensional (1D) fermion systems is checked numerically for spinless fermion model with next-nearest-neighbor interactions. It is shown that for…

We present a mean field theory of composite fermion edge channel transport in the fractional and integer quantum Hall regimes. An expression relating the electro-chemical potentials of composite fermions at the edges of a sample to those of…

The scaling exponent $g$ of the quasiparticle propagator for incompressible fractional quantum Hall states in the Laughlin sequence is expected to be robust against perturbations that do not close the gap. Here we probe the topological…

We investigate quantum transport in graphene/InSe heterostructures and find major asymmetries in the longitudinal resistance ($R_{xx}$) and vanishing $R_{xx}$ peaks at high magnetic fields, particularly at the charge-neutrality point. Our…

We examine charge fractionalization by chiral separation in a one-dimensional fermion system described by Luttinger liquid theory. The focus is on the question of whether the fractional charges are quantum mechanically sharp, and in the…

We study the non-equilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL,…

One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a…

We investigate the homogeneous chiral edge theory of the filling $\nu=4/3$ fractional quantum Hall state, which is parameterized by a Luttinger liquid velocity matrix and an electron tunneling amplitude (ignoring irrelevant terms). We…

We verify the validity of the Cohen-Gallavotti fluctuation theorem for the strongly correlated problem of charge transfer through an impurity in a chiral Luttinger liquid, which is realizable experimentally as a quantum point contact in a…

We report on microscopic numerical studies which support the chiral Luttinger liquid theory of the fractional Hall edge proposed by Wen. Our calculations are based in part on newly proposed and accurate many-body trial wavefunctions for the…

This article reports on our microscopic investigations of the edge of the fractional quantum Hall state at filling factor $\nu=1/3$. We show that the interaction dependence of the wave function is well described in an approximation that…

Current Luttinger liquid edge state theories for filling $\nu=2/3$ predict a non-universal Hall conductance, in disagreement with experiment. Upon inclusion of random edge tunnelling we find a phase transition into a new…

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some…

We discuss quantum Hall effects in a gapped insulator on a periodic two-dimensional lattice. We derive a universal relation among the the quantized Hall conductivity, and charge and flux densities per physical unit cell. This follows from…

Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor 1/k (with k an odd integer) to the insulator have indicated a ``quantized Hall insulator'' (QHI) behavior: while the longitudinal resistivity…

We investigate the generic transport in a one-dimensional strongly correlated fermionic chain beyond linear response. Starting from a Gaussian wave packet with positive momentum on top of the ground state, we find that the numerical time…

We elucidate the nature of neutral collective excitations of fractional quantum Hall liquids in the long-wavelength limit. We demonstrate that they are chiral gravitons carrying angular momentum - 2, which are quanta of quantum motion of an…

We elaborate on a single-mode description of the ballistic charge transport through a narrow constriction in a compressible (composite fermion) Quantum Hall liquid. In the presence of long-range Coulomb interactions we find logarithmic…