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Register a new userSingle-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain
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Quantum entanglement and correlations in the spin-1 Heisenberg chain with single-ion anisotropy are investigated using the quantum renormalization group method. Negativity and quantum discord (QD) are calculated with various anisotropy parameters $bigtriangleup$ and single-ion anisotropy parameters $D$. We focus on the relations between two abovementioned physical quantities and on transitions between the Neel, Haldane, and Large-D phases. It is found that both negativity and QD exhibit step-like patterns in different phases as the size of the system increases. Interestingly, the single-ion anisotropy parameter $D$, which can be modulated using nuclear electric resonance (2020 textit{Nature} textbf{579} 205), plays an important role in tuning the quantum phase transition (QPT) of the system. Both the first partial derivative of the negativity and quantum discord with respect to $D$ or $bigtriangleup$ exhibit nonanalytic behavior at the phase transition points, which corresponds directly to the divergence of the correlation length. The quantum correlation critical exponents derived from negativity and QD are equal, and are the reciprocal of the correlation length exponent at each critical point. This work extends the application of quantum entanglement and correlations as tools for depicting QPTs in spin-1 systems.
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We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing to calculate the ground state. Using this approach, the phase boundaries between the antiferromagnetic N{e}el, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetery protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in, which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.
We consider the dimerized spin-1 $XXZ$ chain with single-ion anisotropy $D$. In absence of an explicit dimerization there are three phases: a large-$D$, an antiferromagnetically ordered and a Haldane phase. This phase structure persists up to a critical dimerization, above which the Haldane phase disappears. We show that for weak dimerization the phases are separated by Gaussian and Ising quantum phase transitions. One of the Ising transitions terminates in a critical point in the universality class of the dilute Ising model. We comment on the relevance of our results to experiments on quasi-one-dimensional anisotropic spin-1 quantum magnets.
Recently, it has been proposed that higher-spin analogues of the Kitaev interactions $K>0$ may also occur in a number of materials with strong Hunds and spin-orbit coupling. In this work, we use Lanczos diagonalization and density matrix renormalization group methods to investigate numerically the $S=1$ Kitaev-Heisenberg model. The ground-state phase diagram and quantum phase transitions are investigated by employing local and nonlocal spin correlations. We identified two ordered phases at negative Heisenberg coupling $J<0$: a~ferromagnetic phase with $langle S_i^zS_{i+1}^zrangle>0$ and an intermediate left-left-right-right phase with $langle S_i^xS_{i+1}^xrangle eq 0$. A~quantum spin liquid is stable near the Kitaev limit, while a topological Haldane phase is found for $J>0$.
We demonstrate quantum critical scaling for an $S=1/2$ Heisenberg antiferromagnetic chain compound CuPzN in a magnetic field around saturation, by analysing previously reported magnetization [Y. Kono {it et al.}, Phys. Rev. Lett. {bf 114}, 037202 (2015)], thermal expansion [J. Rohrkamp {it et al.}, J. Phys.: Conf. Ser. {bf 200}, 012169 (2010)] and NMR relaxation data [H. Kuhne {it et al.}, Phys. Rev. B {bf 80}, 045110 (2009)]. The scaling of magnetization is demonstrated through collapsing the data for a range of both temperature and field onto a single curve without making any assumption for a theoretical form. The data collapse is subsequently shown to closely follow the theoretically-predicted scaling function without any adjustable parameters. Experimental boundaries for the quantum critical region could be drawn from the variable range beyond which the scaled data deviate from the theoretical function. Similarly to the magnetization, quantum critical scaling of the thermal expansion is also demonstrated. Further, the spin dynamics probed via NMR relaxation rate $1/T_1$ close to the saturation is shown to follow the theoretically-predicted quantum critical behavior as $1/T_1propto T^{-0.5}$ persisting up to temperatures as high as $k_mathrm{B}T simeq J$, where $J$ is the exchange coupling constant.
We explore the fidelity susceptibility and the quantum coherence along with the entanglement entropy in the ground-state of one-dimensional spin-1 XXZ chains with the rhombic single-ion anisotropy. By using the techniques of density matrix renormalization group, effects of the rhombic single-ion anisotropy on a few information theoretical measures are investigated, such as the fidelity susceptibility, the quantum coherence and the entanglement entropy. Their relations with the quantum phase transitions are also analyzed. The phase transitions from the Y-N{e}el phase to the Large-$E_x$ or the Haldane phase can be well characterized by the fidelity susceptibility. The second-order derivative of the ground-state energy indicates all the transitions are of second order. We also find that the quantum coherence, the entanglement entropy, the Schmidt gap can be used to detect the critical points of quantum phase transitions. Conclusions drawn from these quantum information observables agree well with each other. Finally we provide a ground-state phase diagram as functions of the exchange anisotropy $Delta$ and the rhombic single-ion anisotropy $E$.
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