Using the exact diagonalization technique, we determine the energy spectrum and wave functions for finite chains described by the two-spin (Kugel-Khomskii) model with different types of intersubsystem exchange terms. The obtained solutions provide the possibility to address the problem of quantum entanglement inherent in this class of models. We put the main emphasis on the calculations of the concurrence treated as an adequate numerical measure of the entanglement. We also analyze the behavior of two-site correlation functions considered a local indicator of entanglement. We construct the phase diagrams of the models involving the regions of nonzero entanglement. The pronounced effect of external fields, conjugated to both spin variables in the regions with entanglement, could both enhance and weaken the entanglement depending on the parameters of the models.
Using the exact diagonalization technique, we determine the energy spectrum and wave functions for finite chains described by the two-spin (Kugel-Khomskii) model with different types of intersubsystem exchange terms. The obtained solutions provide the possibility to address the problem of quantum entanglement inherent in this class of models. We put the main emphasis on the calculations of the concurrence treated as an adequate numerical measure of the entanglement. We also analyze the behavior of two-site correlation functions considered a local indicator of entanglement. We construct the phase diagrams of the models involving the regions of nonzero entanglement. The pronounced effect of external fields, conjugated to both spin variables in the regions with entanglement, could both enhance and weaken the entanglement depending on the parameters of the models.
We study the quantum entanglement of the spin and orbital degrees of freedom in the one-dimensional Kugel-Khomskii model, which includes both gapless and gapped phases, using analytical techniques and exact diagonalization with up to 16 sites. We compute the entanglement entropy and the entanglement spectra using a variety of partitions or ``cuts'' of the Hilbert space, including two distinct real-space cuts and a momentum-space cut. Our results show that the Kugel-Khomski model possesses a number of new features not previously encountered in studies of the entanglement spectra. Notably, we find robust gaps in the entanglement spectra for both gapped and gapless phases with the orbital partition, and show these are not connected to each other. The counting of the low-lying entanglement eigenvalues shows that the ``virtual edge'' picture, which equates the low-energy Hamiltonian of a virtual edge, here one gapless leg of a two-leg ladder, to the ``low-energy'' entanglement Hamiltonian, breaks down for this model, even though the equivalence has been shown to hold for a similar cut in a large class of closely related models. In addition, we show that a momentum space cut in the gapless phase leads to qualitative differences in the entanglement spectrum when compared with the same cut in the gapless spin-1/2 Heisenberg spin chain. We emphasize the new information content in the entanglement spectra compared to the entanglement entropy, and using quantum entanglement, we present a refined phase diagram of the model. Using analytical arguments, exploiting various symmetries of the model, and applying arguments of adiabatic continuity from two exactly solvable points of the model, we are also able to prove several results regarding the structure of the low-lying entanglement eigenvalues.
We analyze the quantum entanglement at the equilibrium in a class of exactly solvable one-dimensional spin models at finite temperatures and identify a region where the quantum fluctuations determine the behavior of the system. We probe the response of the system in this region by studying the spin dynamics after projective measurement of one local spin which leads to the appearance of the ``decoherence wave.'' We investigate time-dependent spin correlation functions, the entanglement dynamics, and the fidelity of the quantum information transfer after the measurement.
By Lanczos exact diagonalization and the infinite time-evolving block decimation (iTEBD) technique, the two-site entanglement as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization in the antiferromagnetic Heisenberg (AFH) model under an external field are investigated. With increasing external field, the small size system shows some distinct upward magnetization stairsteps, accompanied synchronously with some downward two-site entanglement stairsteps. In the thermodynamic limit, the two-site entanglement, as well as the bipartite entanglement, the ground state energy, the nearest-neighbor correlations, and the magnetization are calculated, and the critical magnetic field h(c) = 2.0 is determined exactly. Our numerical results show that the quantum entanglement is sensitive to the subtle changing of the ground state, and can be used to describe the magnetization and quantum phase transition. Based on the discontinuous behavior of the first-order derivative of the entanglement entropy and fidelity per site, we think that the quantum phase transition in this model should belong to the second-order category. Furthermore, in the magnon existence region (h < 2.0), a logarithmically divergent behavior of block entanglement which can be described by a free bosonic field theory is observed, and the central charge c is determined to be 1.
Using the trace minimization algorithm, we carried out an exact calculation of entanglement in a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin-21 particles in a two-dimensional triangular lattice coupled through exchange interaction J and subject to an external magnetic field of strength h. We demonstrate, for such a class of two-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the parameter $\ensuremath{\lambda}=h/J$ in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of $\ensuremath{\lambda}$ shows that the system exhibits a quantum phase transition at about ${\ensuremath{\lambda}}_{c}=3.01$, a transition induced by quantum fluctuations at the absolute zero of temperature.
Spins models, despite their simplicity, are known to describe with great precision physical properties of the materials. Of particular interest are the one-dimensional models that present an exact analytical solution, which can be obtained by the transfer matrix method and the decoration-iteration transformation technique. In this thesis, we studied a spin-electron model and two Ising-Heisenberg spin models, where all models are exactly soluble. The first model we investigate concerns a spin-electron diamond chain with Ising spins located on the local sites and mobile electrons dislocated in the interstitial sites under the external magnetic field action. We analyzed the ground states and the correlation between the spins. We show that thermal fluctuations can lead to the emergence of quantum entanglement above the unfrustrated ground states. We also analyze this same model but for different Landé g-factors. We investigated the phase diagrams at zero temperature. We also analyze the magnetization and we show that the magnetic field can cause the emergence of quantum entanglement in some conditions above the non-entanglement ground states. In this same context, we studied the Ising-XYZ diamond model of spin-1/2, with interaction between the second neighbours of the nodal Ising spins, and an external magnetic field applied to the z-axis. We investigate the phase diagram at zero temperature and the quantum entanglement. We notice that the bipartite entanglement between the pairs of Heisenberg interstitial spins in the natural mineral azurite is insensitive to the external magnetic field applied up to approximately 30 K. The third model we studied is a classical-quantum chain consisting of regularly alternating Ising and Heisenberg spins and with two different local anisotropy axes, subject to an applied external magnetic field. We studied the ground states, the magnetization and the susceptibility. It is evidenced that the investigated spin model reproduces magnetic characteristics of the heterobimetallic coordination compound Dy(NO)3(DMSO)2Cu(opba)(DMSO)2. In this thesis we show that the exact soluble spin models can describe with good precision a class of real magnetic materials, which can present interesting magnetic and thermodynamic properties, and quantum entanglement.
Quantum entanglement, as one of the most fundamental features of quantum theory, is the primary source of nonclassical correlations between subsystems and plays a crucial role in quantum energy and information transport phenomena. Investigating the thermal behavior of entanglement in simple systems, such as two-qubit models, provides an effective framework for analyzing the fundamental mechanisms governing quantum heat conduction. In this study, a two-qubit system with anisotropic interactions of the Dzyaloshinskii–Moriya (DM) and KSEA types was examined under an external magnetic field. To characterize the quantum correlations, two complementary measures are employed: negativity as an indicator of entanglement, and local quantum Fisher information (LQFI) as a measure of quantum correlations beyond entanglement. Numerical analysis reveals that the anisotropic structure of spin–spin interactions play a decisive role in the stability of entanglement at various temperatures. In particular, the presence of both DM and KSEA components can enhance the preservation of quantum correlations in the low-temperature regime, whereas the external magnetic field tends to suppress them. These findings provide new insights into the role of quantum correlations in the thermal processes of small-scale systems.