Related papers: Rational indices for quantum ground state sectors
Since the experimental realisation of the integer quantised Hall effect in a two dimensional electron system subject to strong perpendicular magnetic fields in 1980, a central question has been the interrelation between the conductance…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
Outcomes of measurements are characterized by an infinite family of generalized uncertainties, or cumulants, which provide information beyond the mean and variance of the observable. Here, we investigate the cumulants of a conserved charge…
An area law is proved for the Renyi entanglement entropy of possibly degenerate ground states in one-dimensional gapped quantum systems. Suppose in a chain of $n$ spins the ground states of a local Hamiltonian with energy gap $\epsilon$ are…
We theoretically investigate electrical transport in a quantum Hall system hosting bulk and edge current carrying states. Spatially varying magnetic and electric confinement creates pairs of current carrying lines that drift in the same or…
The Lieb-Schultz-Mattis (LSM) theorem and its higher-dimensional extensions forbid the existence of a unique, symmetric, and gapped ground state at fractional fillings in quantum many-body systems with a conserved particle number (or spin…
We present a quantum field theoretical analysis of a $\nu = 1$ quantum Hall system when the effective Land\'e $g$ factor is small. We clearly demonstrate that the ground state of the system is ferromagnetic. We note that it is the short…
Coherent electron transport through a quantum channel in the presence of a general extended scattering potential is investigated using a T-matrix Lippmann-Schwinger approach. The formalism is applied to a quantum wire with Gaussian type…
The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area…
We report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field…
We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall (IQH) regime in terms of many-body physics at higher Landau levels (LL). The results exhibit a strong tendency to avoid the…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
We reexamine the charge transport induced by a weak electric field in two-dimensional quantum Hall systems in a finite, periodic box at very low temperatures. The resulting linear response coefficients consist of the time-independent term…
We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly,…
The Landau level mixing is the key in understanding the mysterious $5/2$ fractional quantum Hall effect in GaAs quantum well. Theoretical calculations with and without Landau level mixing show striking differences. However, the way to deal…
Some theorems on derivatives of the Coulomb density functional with respect to the coupling constant $\lambda$ are given. Consider an electron density $n_{GS}({\bf r})$ given by a ground state. A model Fermion system with the reduced…
Experiments reveal that a confined electron system with two equally-populated layers at zero magnetic field can spontaneously break this symmetry through an interlayer charge transfer near the magnetic quantum limit. New fractional quantum…
Transitions between the quantum Hall state and the Anderson insulator are studied in a two dimensional tight binding model with a uniform magnetic field and a random potential. By the string (anyon) gauge, the weak magnetic field regime is…
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…
Double-layer electron systems in the quantum Hall regime have excitonic condensate ground states when the layers are close together and the total Landau level filling factor is close to an odd integer. In this paper we discuss the…