With The Dzyaloshinskii-moriya Interaction In The Spin Chain Quantum Phase Transitions And Quantum Entanglement

As a many-body system connecting the fields of quantum information theory and the condensed matter physics, quantum spin system has been studied extensively and intensively for its characteristics of quantum entanglement and quantum phase transition. This thesis investigates the property of a special antiferromagnetic Heisenberg chain with the staggered Dzyaloshinskii-Moriya (DM) interactions.When the staggered DM interactions is absent and magnetic field H is applied, the system is in the XY phase at 0 < H <2, the ferromagnetic phase at H >2, and undergoes a second order Pokrovsky-Talapov transition at the point H c= 2. The presence of the staggered DM interactions leads to a significant change in its quantum entanglement and quantum phase transition.At first, by using a simple analytical method, the quantum entanglement of two qubit system ( N =2) was calculated, it show that when the magnitude of the staggered DM interactions D is sufficient small, the concurrence and one-tangle decrease with the increasing of D under the weak field condition ( H << 2), whereas increase under the strong field ( H >> 2) and intermediate field ( H≈2) condition.Secondly, the exact diagonalization (ED) method was used to obtain the spectrum of small size system ( N = 8 and N = 4). The results show that the ground state avoids level-crossing due to the staggered DM interactions, while occurs level-crossing without the staggered DM interactions.This thesis investigates the quantum entanglement and the quantum phase transition in the system by using the Density-Matrix Renormalization Group (DMRG). It is found that the divergence of the derivative of the magnetization near the magnitude of external magnetic field H = 2 disappears when the staggered DM interactions is present. It means that the interaction can remove the field-induced second order quantum phase transition of this system at that point. Also the anomalous behavior of entanglement (include nearest-neightbor concurrence and one-tangle) vanishes. The fact implies that quantum entanglement is a physical quantity which could indicate the quantum phase transition in this model. Further calculation shows that the staggered DM interactions eliminate the divergence of entanglement range at the point H = 2. It means the disappearance of the factorizing point in the model studied, it also reflects the disappearance of the transition point. Due to the presence of the staggered DM interactions, the system never gets in the state with the saturated ferromagnetism under the finite magnetic field, and then holds the spin entanglement. The external magnetic field usually serves as a"entanglement switch"to tune the system, It can turn on the entanglement between neighbor sites in sequence. But the concurrence and entanglement range response sensitively to magnetic field near quantum phase transition point. Since the staggered DM interactions remove the quantum phase transition, the staggered DM interactions avail the tuning of the strength and the range of spin entanglement.