相关论文: Geometric scaling in the quantum Hall system

We study the quantum Hall effect in the surface states of topological insulator in the presence of a perpendicular magnetic field in the framework of edge states. Motion of Dirac fermions will form descrete Landau levels, among which a…

For the fast rotating quasi-two-dimensional dipolar fermions in the quantum Hall regime, the interaction between two dipoles breaks the rotational symmetry when the dipole moment has component in the the plane via being tuned by an external…

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…

We study the critical spin-polarization energy ($\alpha_{\rm C}$) above which fractional quantum Hall states in two-dimensional electron systems confined to symmetric GaAs quantum wells become fully spin-polarized. We find a significant…

"Topological ordered" phases such as gapped quantum spin-liquids and fractional quantum Hall states possess ground state degeneracy on a torus. We show that the topological nature of this degeneracy has interesting consequences for the…

Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the…

We report on the study of the fractional quantum Hall effect at the filling factor 5/2 using exact diagonalization method with torus geometry. The particle-hole symmetry breaking effect is considered using an additional three-body…

Quasiperiodically driven fermionic systems can support topological phases not realized in equilibrium. The fermions are localized in the bulk, but support quantized energy currents at the edge. These phases were discovered through an…

Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…

We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a…

A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…

We review our recent theoretical works on the the quantum spin Hall effect. First we compare edge states in various 2D systems, and see whether they are robust or fragile against perturbations. Through the comparisons we see the robust…

Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…

Until the late 1980s, phases of matter were understood in terms of Landau's symmetry breaking theory. Following the discovery of the quantum Hall effect the introduction of a second class of phases, those with topological order, was…

The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. Here we study the Landau levels and edge states of surface…

We outline a holographic framework that attempts to unify Landau and beyond-Landau paradigms of quantum phases and phase transitions. Leveraging a modern understanding of symmetries as topological defects/operators, the framework uses a…

We propose a scaling model for the universal longitudinal conductivity near the mobility edge for the integer quantum Hall liquid. We fit our model with available experimental data on exponentially activated conductance near the Landau…

Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…

A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…

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…