相关论文: Finite Size Effects and Irrelevant Corrections to …
In Ref.1 (Physical Review B 80, 041304(R) (2009)), we reported an estimate of the critical exponent for the divergence of the localization length at the quantum Hall transition that is significantly larger than those reported in the…
Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ…
We calculated numerically the localization length index $\nu$ for the Chalker-Coddington model of the plateau-plateau transitions in the quantum Hall effect. By taking into account finite size effects we have obtained $\nu = 2.593 \pm…
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…
Motivated by the recent numerical studies on the Chalker-Coddington network model that found a larger-than-expected critical exponent of the localization length characterizing the integer quantum Hall plateau transitions, we revisited the…
The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been vigorously studied in experiments and numerical…
We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order…
The quantum kicked rotor (QKR) model is a prototypical system in the research of quantum chaos. In a spin-$1/2$ QKR, tuning the effective Planck parameter realizes a series of transitions between dynamical localization phases, which closely…
We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic…
The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are…
We study the critical behavior near the integer quantum Hall plateau transition by focusing on the multifractal (MF) exponents $X_q$ describing the scaling of the disorder-average moments of the point contact conductance $T$ between two…
Machine learning has been successfully applied to identify phases and phase transitions in condensed matter systems. However, quantitative characterization of the critical fluctuations near phase transitions is lacking. In this study we…
Finite size corrections to scaling laws in the centers of Landau levels are studied systematically by numerical calculations. The corrections can account for the apparent non-universality of the localization length exponent $\nu{}$. In the…
Fractional quantum Hall (FQH) phases emerge due to strong electronic interactions and are characterized by anyonic quasiparticles, each distinguished by unique topological parameters, fractional charge, and statistics. In contrast, 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)).…
Finite size fluctuations are a crucial ingredient in kinetic theory of long-range interacting collisionless systems. In this Letter, we introduce a phenomenological theory which predicts an anomalous scaling close to marginal stability for…
Once the fractional quantum Hall (FQH) state for a finite size system is put on the surface of a cylinder, the distance between the two ends with open boundary conditions can be tuned as varying the aspect ratio $\gamma$. It scales linearly…
Extreme-value fluctuations at quantum critical points remain poorly understood in the presence of strong correlations and openness. At the integer quantum Hall transition in the open Chalker--Coddington network, we show that the maximal…
Finite-size scaling is investigated in detail around the critical point in the heavy-quark region of nonzero temperature QCD. Numerical simulations are performed with large spatial volumes up to the aspect ratio $N_s/N_t=12$ at a fixed…
Recent high-precision results for the critical exponent of the localization length at the integer quantum Hall (IQH) transition differ considerably between experimental ($\nu_\text{exp} \approx 2.38$) and numerical ($\nu_\text{CC} \approx…