Quantum Phase Transition In Strongly Correlated Electron System

Quantum phase transition(QPT)in strongly correlated electron system is an important topic in the condensed matter physics.Various kinds of interactions in the system compete with each other,which makes the phase diagram extremely rich.The underlying physics has attracted much attention among condensed matter physics community.In this thesis,we address the QPTs and quantum critical phenomena in the one-dimensional XY model and Heisenberg XYZ model under the interplay of the magnetic field and the Dzyaloshinskii-Moriya(DM)interactions.We use the discontinuity in the derivative of energy and proper order parameters to study the QPTs.Also quantum information measures are adopted to investigate the quantum critical behavior.First,we study the one-dimensional spin-1/2 XY model with the external magnetic field and DM interactions.We use Jordan-Winger transformation to solve the XY model analyti-cally and obtain the ground-state energy as well as the wave function.Then we can identify the critical points and depict the phase diagram.By studying the two-point correlation func-tions,we scrutinize the properties of each phase.We also calculate the quantum entangle-ment and quantum coherence of the XY model,and find that the QPT points can be identified by the quantum entanglement and the quantum coherence.The results show that the entan-glement entropy will converge to a constant with increaseing system size when the system is in the gapped phase.However,when the system is in the gapless phase,the entanglement entropy will present a logarithmic divergence with respect to the system size.Besides,we calculate the entropy and the heat capacity of XY model at finite temperature.The peaks of the entropy and the heat capacity are found to vary with the increasing temperature.Further-more,we study the entanglement dynamics of the XY chain when it is coupled to two qubits and when it is periodically driven by the magnetic field.In addition,we also study the one-dimensional Heisenberg XYZ model under the inter-play of the external magnetic field and DM interactions.Since this Hamiltonian cannot be solved analytically,we use the mean-field approximations to calculate the ground-state en-ergy and the correlation functions self-consistently.Based on the numerical calculations,we also use the quantum entanglement and the quantum coherence to study the quantum critical behavior of this model,and find that the QPT points can be identified by the quantum entan-glement and the quantum coherence.Similarly,we find when the z-z interaction is weak,the positions of critical lines are modified comparing with the counterpart XY model,but the phase diagram does not change qualitatively.