相关论文: Modeling Disordered Quantum Systems with Dynamical…
An overview of the random network model invented by Chalker and Coddington, and its generalizations, is provided. After a short introduction into the physics of the Integer Quantum Hall Effect, which historically has been the motivation for…
The Chalker-Coddington network model is often used to describe the transport properties of quantum Hall systems. By adding an extra channel to this model, we introduce an asymmetric model with profoundly different transport properties. We…
We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. The novel feature of our network model is that in addition to a weak topological…
The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility…
Transport phenomena play a crucial role in modern physics and applied sciences. Examples include the dissipation of energy across a large system, the distribution of quantum information in optical networks, and the timely modeling of…
We study a number of hierarchical network models related to the Chalker-Coddington model of quantum percolation. Our aim is to describe the physics of the quantum Hall transition. The hierarchical network models are constructed by combining…
We study the transport properties of disordered two-dimensional electron systems with a perfectly conducting channel. We introduce an asymmetric Chalker-Coddington network model and numerically investigate the point-contact conductance. We…
The directed network model describing chiral edge states on the surface of a cylindrical 3D quantum Hall system is known to map to a one-dimensional quantum ferromagnetic spin chain. Using the spin wave expansion for this chain, we…
We study a quantum network percolation model which is numerically pertinent to the understanding of the delocalization transition of the quantum Hall effect. We show dynamical localization for parameters corresponding to edges of Landau…
We review the time evolution of wavepackets at the metal-insulator transition in two- and three-dimensional disordered systems. The importance of scale invariance and multifractal eigenfunction fluctuations is stressed. The implications of…
The diffusion of electronic wave packets in one-dimensional systems with on-site, binary disorder is numerically investigated within the framework of a single-band tight-binding model. Fractal properties are incorporated by assuming that…
We introduce a network model to describe two-dimensional disordered electron systems with spin-orbit scattering. The network model is defined by a discrete unitary time evolution operator. We establish by numerical transfer matrix…
Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used…
On the basis of the Chalker-Coddington network model, a numerical and analytical study is made of the statistics of point-contact conductances for systems in the integer quantum Hall regime. In the Hall plateau region the point-contact…
We study the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice described by the extended Fermi-Hubbard model, based on tensor network simulations. Considering different initial states, namely…
Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum…
In this paper we propose a new $S$-matrix approach to numerical simulations of network models and apply it to random networks that we proposed in a previous work 10.1103/PhysRevB.95.125414. Random networks are modifications of the…
We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 56 1422 (1997); Arovas et al., PRB 56, 4751 (1997)).…
Generative models realized with machine learning techniques are powerful tools to infer complex and unknown data distributions from a finite number of training samples in order to produce new synthetic data. Diffusion models are an emerging…
We present a Machine Learning approach to solve electronic quantum transport equations of one-dimensional nanostructures. The transmission coefficients of disordered systems were computed to provide training and test datasets to the…