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Recent developments in the scaling theory of the integer quantum Hall effect are discussed. In particular, the influence of electron-electron interactions on the critical behavior are studied. It is further argued that recent experiments on…
In this article we review the quantum Hall physics of graphene based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed…
Ultra-cold atomic systems are among the most promising platforms that have the potential to shed light on the complex behavior of many-body quantum systems. One prominent example is the case of a dense ensemble illuminated by a strong…
Ultracold atom research presents many avenues to study problems at the forefront of physics. Due to their unprecedented controllability, these systems are ideally suited to explore new exotic states of matter, which is one of the key…
We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in the…
The field of ultracold quantum matter has burgeoned over the last few decades, thanks to the growing capabilities for atomic systems to be probed and manipulated with exquisite control. Researchers can now precisely create and study quantum…
The Laughlin state is an ansatz for the ground state of a system of 2D quantum particles submitted to a strong magnetic field and strong interactions. The two effects conspire to generate strong and very specific correlations between the…
The quantum Hall effect is investigated in a high-mobility two-dimensional electron gas on the surface of a cylinder. The novel topology leads to a spatially varying filling factor along the current path. The resulting inhomogeneous…
Nearing a century since its inception, quantum mechanics is as lively as ever. Its signature manifestations, such as superposition, wave-particle duality, uncertainty principle, entanglement and nonlocality, were long confronted as weird…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
These lecture notes attempt to explain the main ideas of the theory of the quantum Hall effect. The emphasis is on the localization and interaction physics in the extreme quantum limit which gives rise to the quantum Hall effect. The…
The quantum Hall effect occuring in two-dimensional electron gases was first explained by Laughlin, who envisioned a thought experiment that laid the groundwork for our understanding of topological quantum matter. His proposal is based on a…
A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states…
Of great recent interest in condensed matter physics are phenomena of coexistence of quantum and classical properties in the same material. Such duality occurs in certain mixed-spin antiferromagnets composed of quantum spin chains…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
An effective Hamiltonian for the study of the quantum Hall effect is proposed. This Hamiltonian, which includes a ``current-current" interaction has the form of a Hamiltonian for a conformal field theory in the large $N$ limit. An order…
Strongly interacting topological matter exhibits fundamentally new phenomena with potential applications in quantum information technology. Emblematic instances are fractional quantum Hall states, where the interplay of magnetic fields and…
The goal of this article is to review developments regarding the use of ultra-cold atoms as quantum simulators. Special emphasis is placed on relativistic quantum phenomena, which are presumably most interesting for the audience of this…
Bringing gravity into a quantum-mechanical framework is likely the most profound remaining problem in fundamental physics. The "unitarity crisis" for black hole evolution appears to be a key facet of this problem, whose resolution will…
In this paper, we present a novel semi-classical theory of the electrostatic and magnetostatic fields and explain the nonlocality problem in the context of the Aharonov-Bohm effect [1]. Specifically, we show that the electrostatic and the…