Related papers: Dual Response Models for the Fractional Quantum Ha…
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to…
This review talk focusses on some of the interesting developments in the area of superstring compactification that have occurred in the last couple of years. These include the discovery that ``mirror symmetric" pairs of Calabi--Yau spaces,…
We construct an effective topological Landau-Ginzburg theory that describes general SU(2) incompressible quantum liquids of strongly correlated particles in two spatial dimensions. This theory characterizes the fractionalization of…
The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding…
We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the…
In this paper, we develop a unified theory for describing Hall effect in various electronic systems based on a pure electron picture (without the hole concept). We argue that the Hall effect is the magnetic field induced symmetry breaking…
The concept of F-invariance, which previously arose in our analysis of the integral and half-integral quantum Hall effects, is studied in 2+2\epsilon spatial dimensions. We report the results of a detailed renormalization group analysis and…
A conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional…
We construct effective field theories of the quantum skyrmion Hall effect from matrix Chern-Simons theory for $N$ electrons, corresponding to matrix dimension $N$. We first consider a quantum Hall droplet within finite $N$ matrix…
We show that the quantum Hall wave functions for the ground states in the Jain series can be exactly expressed in terms of correlation functions of local vertex operators, V_n, corresponding to composite fermions in the n:th…
Methods that are devised to achieve reversal of quantum dynamics in time have been named "quatum time mirrors". Such a time mirror can be considered as a generalization of Hahn's spin echo to systems with continuous degrees of freedom. We…
Mixed dimensional theories have been used to describe condensed matter systems where fermions are constrained to a plane while the gauge fields they interact with remain four-dimensional. Here we investigate dynamical breaking of chiral…
We theoretically report that, with \textit{in-plane} magnetization, the quantum anomalous Hall effect (QAHE) can be realized in two-dimensional atomic crystal layers with preserved inversion symmetry but broken out-of-plane mirror…
We construct effective field theories for gapped quantum Hall systems coupled to background geometries with local Galilean invariance i.e. Bargmann spacetimes. Along with an electromagnetic field, these backgrounds include the effects of…
This thesis explores the application of differential geometric and general relativistic techniques to deepen our understanding of quantum mechanical systems. We focus on three systems, employing these mathematical frameworks to uncover…
The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder, and…
At variational level in the framework of dimensional reduced 'U_e(1)\times U_g(1)' electromagnetism it is considered an anyon Landau-Ginzburg Chern-Simons model for the fractional Hall effect. The collective gauge fields are due to…
We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates…
We show that ultra-cold atoms with synthetic spin-orbit coupling in Raman lattices can be used as versatile quantum simulators to explore the connections between correlated Chern insulators and strongly-coupled four-Fermi field theories…
We have studied the partially spin-polarized fractional quantum Hall states using Chern Simon's theory and plasma picture proposed by Halperin. Using these theoretical techniques we have tried to find the stable polarized states of…