Trace Distance Discord And Quantum Criticality In Spin Diamond Structure

Quantum correlation has attracted much attention in quantum information.It is very important for quantum telecommunication and quantum computation.In 1990 s,the quantum correlation of quantum states has been found that it includes entanglement and other kinds of non-classical correlation.Theoretical calculations and experiments show that such kinds of non-entangled quantum correlation also play important roles in some quantum information processes.Many methods of measurement of quantum correlation have been proposed.Such typical quantum correlations include concurrence used in quantum entanglement,quantum discord used in quantum correlation and so on.Recently,several researches prove that it is convenient to quantify the quantum correlation between two qubit states by distance measures.One of this kind of methods has been paid much attention.Such a metric is the trace distance,which uses the 1-norm.Here we refer to this particular measure as the trace distance discord(TDD).At finite temperature,this method can perform well in decoherence system.Moreover,it can quantify the quantum correlation better in Heisenberg spin chain and detect the quantum phase transition(QPT)more accurately in it.As a result,this paper is devoted to the TDD as a measurement tool to characterize quantum correlation and QPT in IsingHeisenberg spin structure.In this paper,the first two chapters mainly introduce the development of quantum mechanics and quantum information.Some basis concepts about quantum information will be presented and the concept of trace distance discord will be highlighted.In the third chapter,TDD and QPT in Ising-XXZ spin diamond structure at finite temperature will be studied.The corresponding reduced density matrix can be solved exactly by using the decoration transformation together with the usual transfer matrix technique.The quantity of detecting the QPT in the model will be assessed by comparing with other measurement of quantum correlation and will be proved that it is very accurate and reliable to denote the quantum critical behaviors at finite temperatures.In the fourth chapter,TDD will be used to quantify the quantum correlation in Ising-Heisenberg spin diamond structure with XY anisotropy interaction.By quantitatively analyzing each parameter,we can prove again that TDD can detect quantum phase transition well.Moreover,it will be found that quantum correlation will be suppressed under strong magnetic field.In summary,the magnetic field and the anisotropy parameter can decrease or increase quantum correlation.In addition,TDD can detect more quantum correlation across wider areas in the system.It is of great significance to the research on quantum information.