Study On Critical Exponents Of A Quantum Ising Chain With Long-range Interactions

A quantum phase transition which can be characterized by critical exponent plays a signif icant role in the study of quantum behavior at zero temperature.The density-matrix renormalization group technique is one of the most powerful tools in the exploration of the ground state and critical behaviors of one-dimensional or quasi-one-dimensional quantum many-body system.The fidelity susceptibility which can be used to describe the level of similarity of two quantum states is a concept of Quantum information.The nonanalyticity of the quantum many-body system at the critical value can result in a large and qualitative difference of ground wave function close to the critical point.Hence the fidelity susceptibility can be used to describe quantum phase transitions and to investigate the critical exponents of quantum many-body systems.This thesis uses the fidelity susceptibility obtained by exact diagonalization and density-matrix renormalization group method to investigate the critical behaviors of a long-range quantum ferromagnetic Ising chain with a 1?r~? algebraically decaying interaction.We find the critical exponents calculated by above method change monotonically for intermediatebetween the mean-field universality class and the short-range ferromagnetic Ising universality class and are in accord with recent results obtained from renormalization-group theory.On the other hand,this thesis obtains the critical value for 5?3<?<3 by means of the finite-size scaling of the fidelity susceptibility.We study the critical exponents of a long-range interacting quantum ferromagnetic Ising chain for ?<1 as well.In addition,we study the change of the central charge by varying the transverse field in the region of monotonically varying universality class with the concept of the entanglement entropy,and the phase diagram with respect to ? and transverse field h for a small size system obtained by above method is compared with that obtained by the way of fidelity susceptibility.Our work provides the feasibility of using the concept of fidelity susceptibility to explore the critical exponents of a long-range interacting quantum ferromagnetic Ising chain with numerical techniques.