Thermoelectric Hall Conductivity Of The Fractional Quantum Hall Systems On A Disk

The study of quantum Hall effect in two-dimensional electron gas with low temperature and strong magnetic field has become an extremely important research topic in the past 40 years.As a typical multi-electron strong correlation problem,the traditional single-electron approximation or perturbation theory cannot explain the effect,and the physical images of the fractional quantum hall states with many different filling factors are quite different.Fractional quantum hall state completely introduced by the interaction between electronic,it contains the relative between electronics and electronic intrinsic properties of topology structure,can be used to reveal the ordinary topological properties,like fractional charge up and score statistics,especially in some special filling factor,the fractional quantum hall can produce Majorana zero mode excitation and non-Abelian statistics,The macroscopic external expression of its topological structure can show the characteristics of superfluidity.As one of the important challenges in the field of condensed matter physics,fractional quantum hall state has thus triggered scholars' exploration and understanding of new matter and new quantum state,and related research has won the Nobel Prize in Physics for 1985,1998 and 2016.In fractional quantum Hall fluids,the bulk is an insulator with an energy gap,while the low energy excitation in the bulk is a neutral Magneto-roton excitation(also described as a pair of particle-hole excitation).Because of the interaction between bulk and edge,the physics of edge states plays an important role in revealing the topological properties of bulk.The sample of the fractional quantum hall,often can't avoid the existence of the edge,unless you use disk geometry,therefore this thesis we introduced based on the disk geometry structure under different filling factor fractional quantum hall spectroscopy and entanglement spectrum edge reconstruction,shows bound potential weaker than interaction happens when the edge of the refactoring.After the edge reconstruction,? in the current and voltage power law predicted by CLL theory is no longer universal.Therefore,the phenomenon of edge reconstruction is very important for the measurement of the topological order of fractional quantum Hall effect.Theoretically and experimentally,it has been proved that the universal CLL law,or the correspondence between edge and bulk,is only valid when there is no edge reconstruction.In addition,as an important means to describe the properties of topological quantum states theoretically,the entanglement spectrum of the subsystem,namely the eigenvalue energy spectrum of the system's reduced density matrix,has been proved to be a powerful tool to detect the topological order,which is closely related to the topological properties of the system.Recent theoretical work shows that the entanglement spectrum can also be reconstructed while the real space cutting of a rotatingly symmetric disk is maintained.In the case of real space cutting,the critical area of the subsystem corresponds to the size of the associated hole and also corresponds to the minimum of the edge velocity in the entanglement spectrum.This paper study the fractional quantum hall state in the thermal transport properties of finite temperature,mainly in the disk,and calculate the geometric fractional quantum hall in the state of thermal conductivity hall,especially studied the thermal conductivity in low temperature part of hall scaling behavior,compared to under no boundary circle geometry as a result,we in the case of the existence of the edge,It is found that the edge excitation dominates the thermal Hall conductivity behavior at low temperature,which breaks the universal power law of thermal conductivity.We calculate the entangled spectrum of the model wave function in real space by changing the area of the subsystem in order to consider the influence of the edge states.We found that under the non-Abelian Moore-Read state,the influence of Majorana neutral edge mode at low temperature is more significant than that of charge mode.Therefore,Majorana neutral edge mode has important significance for the thermal hall conductivity and the scale behavior of the dominant low temperature part.This partly explains why non-abelian signals appear in low temperature thermal Hall transport experiments.In the field of condensed matter physics,the research on the fractional quantum Hall state with filling factor of 5/2 has found the non-Abelian topological quantum state required by topological quantum computer,in which the quasiparticle excitation meets the requirements of topological quantum computing,which has attracted extensive attention of researchers.But up to now,the specific form of the ground state wave function of 5/2 state has not been fully confirmed experimentally.Numerical verification of the ground state properties of 5/2 FQH state has also gone through a long process,but the conclusion is still not reached.In this paper,we construct the Hamiltonian which satisfies the symmetry of particle holes by exchanging them,and find the quantum state which satisfies the symmetry of particle holes.The ground states were obtained by precise diagonalization and compared with PF and APF states.The ground state properties of non-Abelian 5/2 states were initially understood.