Related papers: Quantum Hall effect in a one-dimensional dynamical…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of…
An effective Hamiltonian describing interaction between generic "fast" and a "slow" systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the…
We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges…
We propose a construction of a global phase diagram for the quantum Hall effect. This global phase diagram is based on our previous constructions of visibility diagrams in the context of the Quantum Hall Effect. The topology of the phase…
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical…
The edge states of a sample displaying the quantum Hall effect (QHE) can be described by a 1+1 dimensional (conformal) field theory of $d$ massless scalar fields taking values on a $d$-dimensional torus. It is known from the work of…
A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this work, we present a detailed roadmap on how to simulate a two-dimensional electron…
Using the hierarchy picture of the fractional quantum Hall effect, we study the the ground state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is…
In this Chapter, we give a brief review of the state of the art of theoretical and experimental studies of synthetic magnetic fields and quantum Hall effects in ultracold atomic gases. We focus on integer, spin, and fractional Hall effects,…
With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…
We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic…
In this paper we propose a model of the fractional quantum Hall effect within conventional one-dimensional bosonization. It is shown that in this formalism the resulting bosonized fermion operator corresponding to momenta of Landau gauge…
We discuss the ordinary quantum Hall effect and a higher-dimensional cousin. We consider the dimensional reduction of these effects to 1+1 and 3+1 space-time dimensions, respectively. After dimensional reduction, an axion field appears,…
We present a detailed description of a quantum scalar field theory within a flat spacetime confined to a cavity with perfectly reflecting moving boundaries. Moreover, we establish an equivalence between this time-dependent setting and a…
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…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative…
We consider the quantum Hall effect of two-dimensional electrons with a periodic potential and study the time dependence of the Hall and longitudinal currents when the electric field is applied abruptly. We find that the currents oscillate…