Localization and Kosterlitz-Thouless Transition in Disordered Graphene

Surface properties at the Kosterlitz-Thouless transition

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent eta of the order parameter correlation function and its surface equivalent eta_parallel at the Kosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) = 1/4 is easily recovered even with systems of relatively small sizes, since the shape effects are encoded in the conformal mapping. The exponent associated to the surface correlations is similarly obtained eta_1(T_…

二维量子逾渗中的Berezinskii-Kosterlitz-Thouless转变与多重分形临界相

Berezinskii-Kosterlitz-Thouless Transition and Multifractal Critical Phase in Two-Dimensional Quantum Percolation

本研究通过数值分析二维量子逾渗模型，发现多重分形临界相介导局域到退局域转变，并识别出BKT转变与幂律型转变，证明该模型与安德森杂质模型属于不同普适类。

无序二维量子化四极绝缘体中的Berezinskii-Kosterlitz-Thouless局域-局域转变

Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators

本文研究了二维量子化四极绝缘体中从拓扑角态到正常Anderson局域态的局域-局域转变，通过有限尺寸标度分析揭示了其Hermitian与非Hermitian系统均具有Berezinskii-Kosterlitz-Thouless类型的临界特征。

Berezinskii-Kosterlitz-Thouless transition in two dimensional random-bond XY model on a square lattice

We perform Monte Carlo simulations to study the two dimensional random-bond XY model on a square lattice. Two kinds of bond randomness with the coupling coefficient obeying the Gaussian or uniform distribution are discussed. It is shown that the two kinds of disorder lead to similar thermodynamic behaviors if their variances take the same value. This result implies that the variance can be chosen as a characteristic parameter to evaluate the strength of the randomness. In addition, the Berezinskii-Kosterlitz-Thouless transition temperature decreases as the variance increases and the transition…

Nonequilibrium Kosterlitz-Thouless transition in a three-dimensional driven disordered system

We demonstrate a three-dimensional Kosterlitz-Thouless (KT) transition in the random field XY model driven out of thermal equilibrium. By employing the spin-wave approximation and functional renormalization group approach, in the weak disorder regime, the three-dimensional driven random field XY model is found to exhibit a quasi-long-range order phase, wherein the correlation function shows power-law decay with a non-universal exponent that depends on the disorder strength. This result is consistent with that reported in a previous numerical study. We further develop a phenomenological theory …

How to measure the spatial correlations in disordered Berezinski-Kosterlitz-Thouless transition ?

The Berezinski-Kosterlitz-Thouless transition is a unique two dimensional phase transition, separating two phases with exponentially and power-law decaying correlations, respectively. In disordered systems, these correlations propagate along favorable paths, with the transition marking the point where global coherence is lost. Here we propose an experimental method to probe locally these particular paths in superconducting thin films, which exhibit this transition, and demonstrate theoretically that close to the transition the coherence propagate along a ramified network, reminiscent of a perc…