Related papers: Irrelevant corrections at the quantum Hall transit…
The macroscopic effects of the quantum conformal anomaly are evaluated in a simplified two-dimensional model of gravitational collapse. The effective action and stress tensor of the anomaly can be expressed in a local quadratic form by the…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
The interplay between topology and electronic correlation effects offers a rich avenue for discovering emergent quantum phenomena in condensed matter systems. In this work, starting from the Weyl-Hubbard model, we investigate the quantum…
Using heuristic arguments and numerical simulations it is argued that the critical exponent $\nu$ describing the localization length divergence at the quantum Hall transition is modified in the presence of spin-orbit scattering with short…
We note an implication of chiral Luttinger liquid based edge state description of the fractional quantum Hall effect. By considering several examples that involve backward moving neutral modes, arising from either composite fermions with…
We report new experimental data on the plateau-insulator transition in the quantum Hall regime, taken from a low mobility InGaAs/InP heterostructure. By employing the fundamental symmetries of the quantum transport problem we are able to…
Driven critical dynamics in quantum phase transitions holds significant theoretical importance, and also practical applications in fast-developing quantum devices. While scaling corrections have been shown to play important roles in fully…
The spin and integer quantum Hall effects are two cousins of topological phase transitions in two-dimensional electronic systems. Their close relationship makes it possible to transform spin to integer quantum Hall effect in two-dimensional…
The quantum Hall plateau transition was studied at temperatures down to 1 mK in a random alloy disordered high mobility two-dimensional electron gas. A perfect power-law scaling with \kappa=0.42 was observed from 1.2K down to 12mK. This…
We present a general formula for the topological part of the effective action for quantum Hall systems in higher dimensions, including fluctuations of the gauge field and metric around background fields of a specified topological class. The…
The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
After a brief survey of theoretical concepts for the two-parameter scaling theory in the integer quantum Hall effect regime, a comprehensive set of early, recent and new experimental results on constructing scaling diagrams for conductance…
Quantum Hall inter-plateaux transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents,…
The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…
We have measured the temperature dependence of the longitudinal resistivity $% \rho_{xx}$ of a two-dimensional electron system in the regime of the quantum Hall plateau transition. We extracted the quantitative form of scaling function for…
Plateau-plateau (P-P) and insulator-quantum Hall conductor (I-QH) transitions are observed in the two-dimensional electron system in an AlGaAs/GaAs heterostructure. At high fields, the critical conductivities are not of the expected…
The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states through either sweeping the magnetic field or tuning the carrier density. The recent…
It is shown that the "massless chiral edge excitations" are an integral and universal aspect of the low energy dynamics of the $\vartheta$ vacuum that has historically gone unnoticed. Within the $SU(M+N)/S(U(M) \times U(N))$ non-linear…
We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to…
In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the…