相关论文: Rational indices for quantum ground state sectors
In this letter, we discuss the recently proposed fractional quantum Hall effect in the absence of Landau levels. It is shown that the parton construction can explain all properties of 1/3 state, including the effective charge of…
We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current…
Temperature dependence of the longitudinal and Hall resistance is studied in the regime of localization-delocalization transition. We carry out measurements of a scaling exponent $\kappa$ in the Landau level mixing region at several filling…
We solve models of $N$ species of fermions in the lowest Landau level with $U(N)$-invariant interactions in the $N\gg 1$ limit. We find saddles of the second quantized path integral at fixed chemical potential corresponding to fractional…
In closed systems, the celebrated Lieb-Schultz-Mattis (LSM) theorem states that a one-dimensional locally interacting half-integer spin chain with translation and spin rotation symmetry cannot have a non-degenerate gapped ground state.…
Based on a recently introduced operator algebra for the description of a class of integrable quantum liquids we define the ground states for all canonical ensembles of these systems. We consider the particular case of the Hubbard chain in a…
The low-field quantum Hall effect is investigated on a two-dimensional electron system in an AlGaAs/GaAs heterostructure. Magneto-oscillations following the semiclassical Shubnikov-de Haas formula are observed even when the emergence of the…
The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the…
We present an ongoing development of an existing code for calculating ground-state, steady-state, and transient properties of many-particle systems. The development involves the addition of the full four-index two electron integrals, which…
We construct useful sets of one-particle states in the quantum Hall system based on the von Neumann lattice. Using the set of momentum states, we develop a field-theoretical formalism and apply the formalism to the system subjected to a…
We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our…
The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of…
We use a wave functional approach to calculate the fidelity of ground states in the Luttinger liquid universality class of one-dimensional gapless quantum many-body systems. The ground-state wave functionals are discussed using both the…
The quantum theory of conductivity of semiconductor objects, to which the quantum wells, wires and dots concern, is constructed. Average values of current and charge densities, induced by a weak electromagnetic field, are calculated. It is…
Properly regularized second-order degenerate perturbation theory is applied to compute the contribution of higher Landau levels to the low-energy spectrum of interacting electrons in a disk-shaped quantum dot. At ``filling factor'' near…
We theoretically investigate a quasi-one-dimensional quantum wire, where the lowest two subbands are populated, in the presence of a helical magnetic field. We uncover a backscattering mechanism involving the helical magnetic field and…
We study generic semilinear Schr\"odinger systems which may be written in Hamiltonian form. In the presence of a single gauge invariance, the components of a solution may exchange mass between them while preserving the total mass. We…
We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators,…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
In this paper we construct such a set of `degenerate' Hamiltonians $\hat{H}$, which differ by an `intrinsic' constant but represent different physical systems yet possess the same ground state density. . Thus, although the proof of…