Related papers: Interacting Quantum Topologies and the Quantum Hal…
We introduce the index $\mathcal{N}(\omega_1,\omega_2)$ of a pair of pure states on a unital C*-algebra, which is a generalization of the notion of the index of a pair of projections on a Hilbert space. We then show that the Hall…
We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly.…
Noncommutative geometry governs the physics of quantum Hall (QH) effects. We introduce the Weyl ordering of the second quantized density operator to explore the dynamics of electrons in the lowest Landau level. We analyze QH systems made of…
Representative wave functions, which encode the topological properties of the spin polarized fractional quantum Hall states in the lowest Landau level, can be expressed in terms of correlation functions in conformal field theories. Until…
We propose a new mechanism to explain the quantum anomalous Hall (QAH) effect and the electric-field-induced topological phase transition in AB-stacked MoTe${}_2$/WSe${}_2$ moir\'e heterobilayers at $\nu=1$ hole filling. We suggest that the…
Electrodynamic responses from three-dimensional (3D) topological insulators (TIs) are characterized by the universal magnetoelectric $E\cdot B$ term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is…
We show that the chiral kagome ice manifold exhibits an anomalous integer quantum Hall effect (IQHE) when coupled to itinerant electrons. Although electron-mediated interactions select a magnetically ordered ground state, the full ice…
The QHE is studied in the context of a CFT. An effective field of $N$ ``spins" associated with the cyclotron motion of particles is taken as an order parameter from which an effective Hamiltonian may be defined. This effective Hamiltonian…
Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting…
A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport…
With low-buckled structure for each layer in graphene bilayer system, there breaks inversion symmetry (P-symmetry) for one stacking when both A and B sublattices in top layer are aligned with those in bottom layer. In consideration of…
Recent advances in the Langlands program shed light on a vast area of modern mathematics from an unconventional viewpoint, including number theory, gauge theory, representation, knot theory and etc. By applying to physics, these novel…
text of abstract (Integer quantum Hall effect (IQHE) has been analysed considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted and their variation is studied as a function…
It is shown, that a spectrum generating algebras and wave functions for the integral and fractional quantum Hall effect are related by the non-unitary similarity transformation. This transformation corresponds to the introduction of the…
In 1993 Keski-Vakkuri and Wen introduced a model for the fractional quantum Hall effect based on multilayer two-dimensional electron systems satisfying quasi-periodic boundary conditions. Such a model is essentially specified by a choice of…
The mutual interplay between electron transport and magnetism has attracted considerable attention in recent years, primarily motivated by strategies to manipulate magnetic degrees of freedom electrically, such as spin-orbit torques and…
The conventional theory of the integer quantum Hall effect (IQHE) fails for irrational magnetic fields owing to the breakdown of magnetic translational symmetry. Here, based on the recently proposed incommensurate energy band (IEB) theory,…
The Integer Quantum Hall Effect (IQHE) is a distinctive phase of two-dimensional electronic systems subjected to a perpendicular magnetic field. Thus far, the IQHE has been observed in semiconductor heterostructures and in mono- and…
A novel model of complex quantum harmonic oscillator is found to account for the observed Fractional quantum Hall effect (FQHE). The sequences of the observed FQHE conductivity and charge are explained. The two sequences are found to…
We consider the trial wavefunctions for the Fractional Quantum Hall Effect (FQHE) that are given by conformal blocks, and construct their associated edge excited states in full generality. The inner products between these edge states are…