Studies On Entanglement Entropy, Magnetic And Thermodynamic Properties Of Low-dimensional Magnetic Materials

Entanglement state has extensive and important applications in nearly every aspect of quantum information theory. That how to control it is a key point in the application of quantum information theory. Entanglement state, which can be described by the degree of entanglement, will be attributed to the research of von Neumann entropy at last.In this paper, by using the density matrix renormalization group (DMRG) method for the one-dimensional Hubbard model, we have studied the von Neumann entropy of a quantum system in different conditions. We first discussed the effects of doping on the distribution of entanglement entropy, charge density and spin density along the chain. Then we calculated the spin and entropy distribution in different external magnetic filed, discussed the relationship between them. Our results are important for designing and synthesizing materials with high information exchange.It is found that doping can alter the charge-charge and spin-spin interactions, resulting in charge polarization and a standing-wave like distribution of the spin density alone the chain. These changes lead to the redistribution of the Neumann entropy at last. By comparing the results before and after doping, we find that doping favors increase of the von Neumann entropy and thus also favors the exchange of information along the chain. Furthermore, the results of the spin and entropy distribution in different external magnetic filed indicate that the Neumann entropy mainly show the spin-spin interaction alone the chain in this condition. At the same time, we also find that the external magnetic field (not too large) could affect the degree of entanglement in different parts of the chain, but it could not enhance or suppress the degree of entanglement along the chain as a whole. Thus it could not be used as a method to improve the capability of quantum communication of materials.Moreover, by using the transfer matrix renormalization group (TMRG) method, we theoretically studied the magnetic and thermodynamic properties of a one-dimensional quantum system. Compared with experiment results of these compounds, we investigated the effects of different interactions among the magnetic irons of this quantum system, and it is found that the ferro- and antiferromagnetic interaction affect the magnetic characteristics of the system and play important roles in determining the internal energy and the specific heat at finite temperature. With the increase of antiferromagnetic interaction, the ferromagnetic state is suppressed and the system transfers into an antiferromagnetic state. As far as the internal energy and the specific heat are concerned, the large antiferromagnetic interaction corresponds to a low internal energy and a large specific heat respectively.