Mapping the current-current correlation function near a quantum critical point

作者：Prodan Emil^*; Bellissard Jean

来源：Annals of Physics, 2016, 368: 1-15.

DOI：10.1016/j.aop.2016.01.022

• Current-current correlation function
• Quantum critical behavior
• Disorder
• Integer quantum Hall effect

The current-current correlation function is a useful concept in the theory of electron transport in homogeneous solids. The finite-temperature conductivity tensor as well as Anderson's localization length can be computed entirely from this correlation function. Based on the critical behavior of these two physical quantities near the plateau-insulator or plateau-plateau transitions in the integer quantum Hall effect, we derive an asymptotic formula for the current-current correlation function, which enables us to make several theoretical predictions about its generic behavior. For the disordered Hofstadter model, we employ numerical simulations to map the current-current correlation function, obtain its asymptotic form near a critical point and confirm the theoretical predictions.

• 出版日期2016-5