Based on analytical and numerical approaches, we investigate thermodynamic properties of CuSe2O5 at high magnetic fields which is a candidate for the strong intra-chain interaction in quasi one-dimensional (1D) quantum magnets. Magnetic behavior of the system can be described by the 1D spin-1/2 XXZ model in the presence of the Dzyaloshinskii-Moriya (DM) interaction. Under these circumstances, there is one quantum critical field in this compound. Below the quantum critical field the spin chain system is in the gapless Luttinger liquid (LL) regime, whereas above it one observes a crossover to the gapped saturation magnetic phase. Indications on the thermodynamic curves confirm the occurrence of such a phase transition. The main characteristics of the LL phase are gapless and spin-spin correlation functions decay algebraic. The effects of zero-temperature quantum phase transition are observed even at rather high temperatures in comparison with the counterpart compounds. In addition, we calculate the Wilson ratio in the model. The Wilson ratio at a fixed temperature remains almost independent of the field in the LL region. In the vicinity of the quantum critical field, the Wilson ratio increases and exhibits anomalous enhancement.

We consider an anisotropic spin-1/2 XY Heisenberg chain in the presence of a transverse magnetic field. Selecting the nearest neighbor pair spins as an open quantum system, the rest of the chain plays the role of the structured environment. In fact, the aforementioned system is used as a quantum probe signifying nontrivial features of the environment with which is interacting. We use a general measure that is based on the trace distance for the degree of non-Markovian behavior in open quantum systems. The witness of non-Markovianity takes on nonzero values whenever there is a flow of information from the environment back to the open system. We have shown that the dynamics of the system with isotropic Heisenberg interaction is Markovian. A dynamical transition into the non-Markovian regime is observed as soon as the anisotropy, γ, is applied. At the Ising value of the anisotropy γ = 1.0, all the information flows back from the environment to the system. The additional dynamical transition from the non-Markovian to the Markovian is obtained by applying the transverse magnetic field. In addition, we have focused on the time evolution of the Loschmidtecho return rate function. It is found that a non-analyticity can be seen in the time evolution of the Loschmidt-echo return rate function exactly at the critical points where a dynamical transition from the Markovian to the non-Markovian occurs.

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We study the dynamics of entanglement in the one-dimensional spin-1/2 XY model in the presence of a transverse magnetic field. A pair of spins are considered as an open quantum system, while the rest of the chain plays the role of the environment. Our study focuses on the pair of spins in the system, the edge spins, and the environment. It is observed that the entanglement between the pair of spins in the system decreases and it can transfer to the rest of the spins. For a value of anisotropy leading to the Ising model, the entanglement is completely back to the system by passing time. On the other hand, the entanglement can only be seen under certain conditions between edge spins of the system and the environment. The pair of spins on the edge will be entangled very quickly and it will disappear after a very short time. A pair of spins far from the system was chosen to examine the behavior of entanglement in the environment. As expected, the transmission of entanglement from the system to the environment takes notable time.