Quantum Phase Transition Of Spinor Bosonic Gases Driven By Magnetic Field And Quantum Phase Transition And Local Field Correction Of Electron Gases At Finite Temperature

The essence of natural science is to study the basic principle behind physical phenomena,which is called the first principle.The first principle is to investigate the basic properties and physical processes of the research object from the most basic equations without using any empirical and experimental parameters.Density functional theory is a well-known first principle method.It expresses the complex electron-electron correlation effect of a quantum many-body problem as an exchange-correlation functional,so as to transform the multi-electron problem into a single electron problem.Density functional theory has made remarkable achievements in calculating the physical properties of metals,some kind of semiconductors and insulators,but it is still approximate in dealing with electron correlation effect,so it becomes impossible to accurately describe strong correlation systems.With the development of science and technology and the gradual deepening understanding of related phenomenon,strong correlation system has triggered great and profound changes in many fields,such as high temperature superconductivity,giant magneto resistance materials and ultracold quantum simulation.Therefore,we occupy bosonic dynamical mean-field theory(BDMFT)and path integral Monte Carlo(PIMC)simulation to investigate the dynamic correlation effect in quantum many-body systems.Specifically,this paper utilize three different levels and stages of methodology to deal with dynamic correlation effect.Here we select the appropriate problem in each stage from basic to delicate level,and perform the following work:The first one is about the phase transition and multi-step condensations of spin-1bosonic gases in optical lattices driven by external magnetic field.In this paper,the BoseHubbard model is used to describe the system,and the model is solved by BDMFT.The intricate interplay of spin-dependent interaction,linear Zeeman effect,quadratic Zeeman effect,quantum fluctuation effect and thermal excitations in the considered model makes the corresponding phase diagram complicated and interesting.In this paper,the competition between spin-ordered phases in Mott insulator and super fluid under different conditions is carefully investigated,and their stability and critical conditions of phase transition are also obtained.Interestingly,when studying the multi-step condensations of Zeeman components under the constraint of constant longitudinal magnetization,we found that some Zeeman components showed an abnormal condensation behavior,which is inconsistent with weakly interacting spinor gases.The second one is the quantum phase transition and thermal melting of two-dimensional Wigner crystal.We have performed restricted path integral Monte Carlo(RPIMC)simulations for two-dimensional electron gas(2DEG)under different temperatures,densities and spin polarization.The critical density of quantum melting and critical temperature of thermal melting for Wigner crystal are determined by directly observing the change of structure factor.In addition,different types of node are occupied in RPIMC simulations to obtain the equation of state for different quantum phases of 2DEG.We have also compared our results with recent experiments as well as other ground state quantum Monte Carlo calculations.The last one is the local field correction(LFC)on the ionization potential depression(IPD)of ions in warm dense plasma.LFC accounts for the dynamic correlation effect between free electrons beyond the mean-field approximation,which can be obtained by RPIMC simulations of three-dimensional electron gases.In order to explicitly account for this effect,we incorporate the LFC within a recently established IPD framework through the connection of dynamical structure factor.Our calculation shows that the introduction of LFC brings a nontrivial influence on IPD at warm/hot dense matter conditions.The correlation effect within LFC could provide up to 20% correction to free-electron contribution of IPD in the strong coupling and degeneracy regime.The IPDs of other elements at warm dense matter conditions are also investigated within our approach,with which excellent agreements are observed with other theoretical predictions and experiments.