相关论文: Modular Invariance, Self-Duality and The Phase Tra…

The crossover from the quantum Hall regime to the Hall-insulator is investigated by varying the strength of the diagonal disorder in a 2d tight-binding model. The Hall and longitudinal conductivities and the behavior of the critical states…

A basic result about the dynamics of spinless quantum systems is that the Maryland model exhibits dynamical localization in any dimension. Here we implement mathematical spectral theory and numerical experiments to show that this result…

The Hall conductance $\sigma_{xy}$ of two-dimensional {\it lattice} electrons with random potential is investigated. The change of $\sigma_{xy}$ due to randomness is focused on. It is a quantum phase transition where the {\it sum rule} of…

We present results of numerical studies of spin quantum Hall transitions in disordered superconductors, in which the pairing order parameter breaks time-reversal symmetry. We focus mainly on p-wave superconductors in which one of the spin…

Using the hierarchy picture of the fractional quantum Hall effect, we study the the ground state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is…

The contribution from quantum vacuum fluctuations of a real massless scalar field to the motion of a test particle that interacts with the field in the presence of a perfectly reflecting flat boundary is here investigated. There is no…

There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the…

In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on…

We study the probability distribution of a current flowing through a diffusive system connected to a pair of reservoirs at its two ends. Sufficient conditions for the occurrence of a host of possible phase transitions both in and out of…

This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…

Sharp localization transitions of chiral edge states in disordered quantum wires, subject to strong magnetic field, are shown to be driven by crossovers from two- to one-dimensional localization of bulk states. As a result, the two-terminal…

The phase transitions in the transverse field Ising model in a competing spatially modulated (periodic and oscillatory) longitudinal field are studied numerically. There is a multiphase point in absence of the transverse field where the…

The new integrable quantum spin model is proposed. The model has a biaxial magnetic anisotropy of alternating coupling between spins together with multiple spin interactions. Our model gives the possibility to exactly find thermodynamic…

A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional…

Recent transport experiments in spatially modulated quasi-1D structures created on top of LaAlO$_3$/SrTiO$_3$ interfaces have revealed some interesting features, including phenomena conspicuously absent without the modulation. In this work,…

Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between…

It has been proposed that band-inverted electron-hole bilayers support a phase transition from an insulating phase with spontaneously broken time-reversal symmetry to a quantum spin Hall insulator phase as a function of increasing electron…

Recently, a zero Hall conductance plateau with random domains is experimentally observed in quantum anomalous Hall (QAH) effect. We study the effects of random domains on the zero Hall plateau in QAH insulators. We find the structure…

Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…

The quantum Hall effect is one of the most extensively studied topological effects in solid state physics. The transitions between different quantum Hall states exhibit critical phenomena described by universal critical exponents. Numerous…