Study On The Entanglement Spectrum Edge Reconstruction And Correlation Hole Of Fractional Quantum Hall Liquids

It is nearly 40 years since von Klitzing et al.discovered the integer quantum Hall effect in 1980.The discovery of integer quantum Hall effect opened up the way for the later discovery of various phenomena,especially the later discovery of fractional quantum Hall effect.At the same time,the discovery of the fractional quantum Hall effect promoted the development of the theory of strongly correlated electronic systems,in particular,it revealed the existence of concepts that had previously been the product of theoretical imagination.In this decades,scientists have made a lot of outstanding contribution in this field and developed forward continuously,many previously exist only in a theoretical physicis at new concepts in the brain or old concepts proved to be applicable to the two-dimensional system,such as particle statistics,charged particles,angel particles and Tomonaga Luttinger liquids,etc… and they have been observed,these outstanding research achievements have greatly promoted the development of condensed matter physics since 1980.From an experimental point of view,most of the results are derived from measurements of semiconductor heterostructures with many parameters,such as electron-electron interaction,disorder potential,spin characteristics or edge profiles.These possibilities,as well as new theoretical concepts,provide the basis for the study of the quantum Hall effect.This paper describes the importance of correlation holes for understanding the fractional quantum Hall states.For different fractional quantum Hall states,the correlation holes correspond to "flux units".For example,the fundamental unit of the=1/3 laughlin state is the combination of an correlation hole,that is to say,the three available single particle states,which are occupied only by the particles to which they are attached.In general,the basic unit of a FQH liquid is the "composite boson" of p particles and q quanta,which is a unit similar to a solid.It is very important for us to better understand the properties of the fundamental correlation holes in fractional quantum Hall system.This paper considers the fractional quantum Hall state with the filling factor of? = 1/3 as the main research object in the disk geometry.Based on fractional quantum Hall state at the edge of the energy space reconstruction as the breakthrough point,discussion in the fractional quantum Hall state entanglement space also has the nature of the edge reconstruction,use of real space of the entanglement of the spectrum,change the position of the real space of the cut,found in a subsystem,for a fixed value,as the change of the location of the real space of the cut,the phenomenon of entanglement in the spectrum is edge reconstruction and the hole can be associated with fractional quantum Hall droplet in the accurate.This provides a new perspective for the study of topological properties in quantum quantum Hall states,and also calculates the existence of this possibility in other fractional quantum Hall states,providing certain theoretical support for other possibilities in fractional quantum Hall states and the better application of fractional quantum Hall effect.In addition,the dynamic problems of fractional quantum Hall systems has been a difficult point,this thesis through the radius R of disk geometry on considering the interaction between N electronic in Laughlin is the study of the potential impurities in the liquid,in the lowest landau level to consider at the moment of T = 0 and the impurity potential,when T is not equal to zero potential will take out,considering the dynamics of a single time evolution,further study the effect of the impurity potential on the system,not only will this help a better understanding of electrons in a real system,and can further find more kinetics law of quantum phase transition.