The Study Of Dynamic Quantum Phase Transitions In One-dimensional Quasi-periodic Quantum Spin Systems And Boson Systems

In recent decades,the dynamic behavior of isolated quantum systems has been a hot research topic in statistical physics,quantum physics and condensed matter physics.On the one hand,it can help people understand the basic properties of quantum systems and the basic problems of statistical physics.On the other hand,due to the development of experimental techniques,such as ultra-cold atoms in optical lattices and ion traps,the dynamic behavior of these materials can be observed experimentally.Among the many studies on the dynamics of isolated quantum systems,one of the most interesting topics is the dynamical quantum phase transitions(DQPTs),that is,the non-analytic behavior of physical quantities with the change of time.It was proposed by Heyl et al in2013.Since then,great progress has been made in the research of DQPTs of the quantum subsystem.Theoretically,DQPTs has been found in a number of systems,including the quantum Ising model of the transverse field,XY model,XXZ model,hard core boson model,Kitaev honeycomb model,Floquet system,long-range interacting system and topological system.In addition,DQPTs have been observed in experiments involving trapping ion traps,quantum bit simulators,and optical lattices.Although great progress has been made in the study of DQPTs,most of them are homogeneous DQPTs.The thesis foucs on the DQPTs from three models of generalized Fibonacci sequence,including quantum Ising chain,anisotropic XY chain and the one-dimensional boson model.First,we derive the formulas for the Loschmidt amplitude,Fisher zero and rate functions of the quantum Ising chain in real space,and the DQPTs of this model can be studied by using these formulas.We used the nearest neighbor interaction coefficient J to construct the quasi-periodic quantum Ising model according to the generalized Fibonacci sequence,and studied the DQPTs of the quantum Ising chain by analyzing the Fisher zero and the rate function.When the phase transition point is quenched,there is a phase transition point where the Fisher zero line of each class intersects the imaginary axis at a point under uniform conditions.We find that in the case of weak quasi-periodic,compared with the homogeneous chain,a new Fisher zero appears on the imaginary axis,that is,a new phase transition points appears.With the increase of quasi-periodic intensity,many Fisher zeros appear on the imaginary axis,and the number of phase transition point increases,and these Fisher zeros gradually become a region under the thermodynamic limit.When quenching does not occur at the phase transition point,the Fisher zero will not appear on the imaginary axis in either the case of weak quasi-periodic or strong quasi-periodic,and there is no DQPTs.Next,we also studied the DQPTs of the quantum Ising chain of the first and second class of generalized Fibonacci sequences.We found that these two types of systems were similar to the DQPTs of the quantum Ising chain of the Fibonacci sequence.Then,we derived the formulas of the Loschmidt amplitude,the Fisher zero and the rate function of the anisotropic XY chain in real space.We constructed the quasi-periodic anisotropic XY model with the nearest neighbor interaction coefficient J according to the generalized Fibonacci sequence,and studied the DQPTs of this model by analyzing the Loschmidt amplitude,Fisher zero and rate function.We considered four quenching paths spanning the anisotropic phase change,simultaneously spanning the Ising phase change and the anisotropic phase change,in the ferromagnetic phase and in the paramagnetic phase.For quenching across the anisotropic phase transition,in the uniform case,each class of fisher zero line intersects the imaginary axis at two points,there are two phase transition points.We find that in both the Fibonacci sequence and the two kinds of generalized Fibonacci sequences,in the case of weak quasi-period,a new Fisher zero appears on the imaginary axis,that is,a new phase transition point appears.Similarly,as the quasi-periodic intensity increases,the Fisher zeros gradually becomes a region in the thermodynamic limit.For the cross-ising and anisotropic transformation of quenching,there is a phase change point under uniform condition.We find that in the case of weak quasi-periodic,compared with the uniform chain,a new Fisher zero appears on the imaginary axis,that is,a new phase change point appears.Similarly,when the quasi-periodic intensity is very high,in the thermodynamic limit,the fisher zeros becomes a region on the imaginary axis.For the quenching in the ferromagnetic phase,we choose the path where two phase transition points appear in the homogeneous system.Under this path,when the quasi-periodic strength is weak,the fisher zeros is the same as that under the uniform case,and the system still has only two phase transition points.The quasi-periodic strength is enhanced and a new phase change point appears.When the quasi-periodic intensity is stronger,the phase change point disappears and DQPTs no longer exist.For the quenching in the paramagnetic phase,similarly,we choose the path where two phase transition points appear in the homogeneous system.In the case of weak quasi-periodic,a new phase change point will appear.The phase transition point still exists in a large range of quasi-periodic intensity.Finally,we derive the Loschmidt amplitude and rate functions of the one-dimensional binary heterogeneous boson model,and the DQPTs of this model can be studied by using these formulas.We use the potential construct a one-dimensional binary heterogeneous boson model according to binary order,period two and generalized Fibonacci sequence,and study the DQPTs of this model by analyzing the Loschmidt amplitude and rate function.We find that the distribution of potential is a one-dimensional boson system with equal probability of binary disorder and period of two and generalized Fibonacci sequence(n = 1,m = 2).When the disorder intensity W is large,the absolute value of the Loschmidt amplitude will be approximately equal to 0,and DQPTs will exist in the system.In summary,no matter which binary inhomogeneous one-dimensional boson model is used,DQPTs will appear in the system as long as the distribution of two inpotential is equally probability.