Research Of Topological Quantum Phase In The Extended SSH Model

Landau symmetry breaking theory was regarded as the standard theory to describe all phases and phase transitions.However,in 1989,through a theoretical study of integer and fractional quantum Hall effects and the appearance of topological insulators,that it was necessary to introduce topological order to characterize a large class of new quantum phenomena.Topologically ordered phases open a new window to be explored the mysteries in condensed matter physics.Correlated many body systems play an important role in low dimensional topologically ordered phases,for example,in systems represented by fractional quantum hall effect,strongly correlated interactions are necessary to form topological orders;if the topological orders can be defined in free systems,but there is the main content of our research that it should be stable against strong correlated interaction.The degree of freedom reaches the thermodynamic magnitude to deal with these systems,both mean filed theory and perturbation theory are inappropriate,so numerical methods are very imminent.In this thesis,we will use numerical methods to simulate SSH model of topologically ordered states in low dimensional strongly correlated systems.Firstly,we first give a brief review of the SSH model one dimensional topological states.When turning dimerization parameters,there will undergo a topological quantum phase transition.However,generally the ground state can no longer be solved exactly in the SSH-H model.We study the phase diagram based on the matrix product state(MPS)representation to simulate the physical quantities of different topological states.We find the edge degeneracies are reduced by the perturbation of the weak interactions but remain to be nontrivial.Although the topological boundary state is unstable under the perturbation of the strong interactions,the symmetry protected topological order remains.Secondly,we studied the competition mechanism of different parameters in the SSH model for the first time coupling parameter repulsive particle-interaction and spin-orbit coupling.Entanglement spectrum are employed to study how topological order changes in the phase transition and confirm that the symmetry protected topological order remains in both topological insulator phases.Furthermore,we discuss results about how strongly correlated interactions will affect the stability of topological order,as well as giving a reliable result about the maximum value of interaction strength when topological order remains unbroken.In this work,we find a continuous topological quantum phase transition between two states,and confirm some basic concepts in Landau's second order phase transition theory can be used in these phase.Moreover,the zero temperature phase diagram are investigated and this work may provide some help for the further investigation of topological orders around critical point of topological state.Finally,we studied the effect of topological phase transition with the nearest-neighbour interactions in the SSH-H model,then compared with the topological quantum phases driven by the on-site interactions.From the phase diagram point of view,the strong interactions are used to induce the mechanism of topological phase transitions.