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I present a brief survey of important recent developments in the quantum Hall effect. The review covers both fractional and integer regimes, from an experimentalist's perspective. The topics include direct measurement of fractional charge,…

The gapless edge modes of the Quantum Spin Hall insulator form a helical liquid in which the direction of motion along the edge is determined by the spin orientation of the electrons. In order to probe the Luttinger liquid physics of these…

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the…

We review the construction of a low-energy effective field theory and its state space for "abelian" quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern-Simons theory in 2+1 dimensions on a manifold…

The observed robustly quantized Hall conductance in quantum Hall systems and Chern insulators (CI) have so far been understood in terms of the topology of isolated systems, which are not coupled to leads. It is assumed that the leads act as…

We derive the hamiltonian and canonical structure for arbitrary deformations of a phase space (quantum Hall) droplet on a general manifold of any dimension. The derivation is based on a transformation that decouples the Casimirs of the…

We show that the chiral anomaly of quantum field theories with Dirac fermions subject to an axial background field is an inherent property of kinematics of a perfect classical fluid. Celebrated Beltrami flows (stationary solutions of Euler…

An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this…

We study models of chiral interacting fermions by means of conformal and Bethe-Ansatz techniques, and determine their thermodynamic properties and asymptotic correlation functions. We identify a class of fixed points characterizing the…

We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen as an adaptation of the proof of [1], simplified by making…

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the…

From quantum field theory, we derive the chiral kinetic theory involving nonlinear quantum corrections coupled with spacetime-dependent electromagnetic fields and fluid velocity gradients. An equilibrium Wigner function determined by the…

We show that the dc conductance of a quantum wire containing a Luttinger liquid and attached to non-interacting leads is given by $e^2/h$ per spin orientation, regardless of the interactions in the wire. This explains the recent…

We investigate certain invariance properties of quantum fluids subject to a nonlinear gauge potential. In particular, we derive the covariant transformation laws for the nonlinear potentials under a space-time Galilean boost and consider…

In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…

The long-thought charge Kondo effects have recently been experimentally realized in the quantum Hall regime. This experiment, supported by numerics, exemplifies the realization of two-channel Kondo state, a non-Fermi Liquid, and its…

We discuss the conductance of quantum wires (QW) in terms of the Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge fractionalization scheme which results from the chiral symmetry of the model. We suggest that results of…

We investigate the effect on a Quantum Hall (QH) liquid of its coupling to 3+1 dimensional dynamical electromagnetism, which renders the system gapless. We calculate both the Hall and longitudinal resistances, $\rho_H$ and $\rho_L$, in the…

The Luttinger model of the one-dimensional Fermi gas is the cornerstone of modern understanding of interacting electrons in one dimension. In fact, the enormous class of systems whose universal behavior is adiabatically connected to it are…

Hall and diagonal resistances of bilayer fractional quantum Hall systems are discussed theoretically. The bilayers have electrodes attached separately to each layer. They are assumed to be coupled weakly by interlayer tunneling, while the…