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arXiv:1106.5378 · Physica Scripta

Phase transitions and entanglement properties in spin-1 Heisenberg clusters with single-ion anisotropy

Vahagn Abgaryan, N.S. Ananikian, L N Ananikyan, ARMEN N. KOCHARIAN

Published Apr 18, 2011• 16 citations
arXivHTMLPDF

Abstract

The incipient quantum phase transitions of relevance to nonzero fluctuations and entanglement in Heisenberg clusters are studied in this paper by exploiting negativity as a measure in bipartite and frustrated spin-1 anisotropic Heisenberg clusters with bilinear–biquadratic exchange, single-ion anisotropy and magnetic field. Using the exact diagonalization technique, it is shown that quantum critical points signaled by qualitative changes in behavior of magnetization and particle number are ultimately related to microscopic entanglement and collective excitations. The plateaus and peaks in spin and particle susceptibilities define the conditions for a high/low-density quantum entanglement and various ordered phases with different spin (particle) concentrations.

DOI
10.1088/0031-8949/83/05/055702

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The incipient quantum phase transitions of relevance to nonzero fluctuations and entanglement in Heisenberg clusters are studied in this paper by exploiting negativity as a measure in bipartite and frustrated spin-1 anisotropic Heisenberg clusters with bilinear–biquadratic exchange, single-ion anisotropy and magnetic field. Using the exact diagonalization technique, it is shown that quantum critical points signaled by qualitative changes in behavior of magnetization and particle number are ultimately related to microscopic entanglement and collective excitations. The plateaus and peaks in spin and particle susceptibilities define the conditions for a high/low-density quantum entanglement and various ordered phases with different spin (particle) concentrations.
Abstract In this paper we investigate the ability of the generalized concurrence as a quantum entanglement measure to describe the quantum and thermal phase transitions in the spin-1 Heisenberg model with bilinear and biquadratic interactions and single-ion anisotropy terms, under a magnetic field. Calculations are performed for two and three spin chains based on the exact diagonalization method. We show that in the near vicinity of the zero temperature, the generalized concurrence changes abruptly from a finite non-zero value to zero by changing the parameters of the model. This is signature of a quantum phase transition that is carefully justified by studying the thermodynamic functions such as magnetization, particle number, particle susceptibility and magnetic susceptibility. The critical points are found and various ordered phases are discussed.
We investigate thermal and non-thermal quantum correlations in the one-dimensional spin-1 bilinear-biquadratic Heisenberg model. Using tools from quantum information theory-such as generalized concurrence, negativity, and various measures of quantum, classical, and total correlations in bipartite states-we demonstrate that these measures effectively identify quantum phase transitions (QPTs) at critical points. Our negativity analysis reveals nearly identical results at zero or very low temperatures. Importantly, we find that partial concurrence, defined with the reduced density matrix [Formula: see text], detects more quantum critical points than total concurrence. Additionally, we argue that spin chains with an odd number of spins are more effective than those with an even number in identifying QPTs.
Abstract 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 △ and single-ion anisotropy parameters D . We focus on the relations between two abovementioned physical quantities and on transitions between the Néel, 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 Nature 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 QD with respect to D or △ 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.
Abstract Motivated by the fact that the study of disordered phases at zero temperature is of great interest, I study the spin-one quantum antiferromagnet with a next-nearest neighbor interaction on a triangular lattice with bilinear and biquadratic exchange interactions and a single ion anisotropy, using a SU(3) Schwinger boson mean-field theory. I calculate the critical properties, at zero temperature, for values of the single ion anisotropy parameter D above a critical value D C , where a quantum phase transition takes place from a higher D disordered phase to a lower D ordered phase.
We explore numerically the inverse participation ratios in the ground state of one-dimensional spin-1 XXZXXZXXZ chains with the rhombic single-ion anisotropy. By employing the techniques of density-matrix renormalization group, effects of the rhombic single-ion anisotropy on various 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 YYY-N\'eel phase to the large-Ex{E}_{x}Ex​ 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, and the inverse participation ratios can be used to detect the critical points of quantum phase transitions. Results 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 $\mathrm{\ensuremath{\Delta}}$ and the rhombic single-ion anisotropy EEE.
The bipartite entanglement in pure and mixed states of a quantum spin-1 Heisenberg dimer with exchange and uniaxial single-ion anisotropies is quantified through the negativity in a presence of the external magnetic field. At zero temperature the negativity shows a marked stepwise dependence on a magnetic field with two abrupt jumps and plateaus, which can be attributed to the quantum antiferromagnetic and quantum ferrimagnetic ground states. The magnetic-field-driven phase transition between the quantum antiferromagnetic and quantum ferrimagnetic ground states manifests itself at nonzero temperatures by a local minimum of the negativity, which is followed by a peculiar field-induced rise of the negativity observable in a range of moderately strong magnetic fields. The rising temperature generally smears out abrupt jumps and plateaus of the negativity, which cannot be distinguished in the relevant dependencies above a certain temperature. It is shown that the thermal entanglement is most persistent against rising temperature at the magnetic field, for which an energy gap between a ground state and a first excited state is highest. Besides, temperature variations of the negativity of the spin-1 Heisenberg dimer with an easy-axis single-ion anisotropy may exhibit a singular point-kink, at which the negativity has discontinuity in its first derivative. The homodinuclear nickel complex [Ni2(Medpt)2(μ-ox)(H2O)2](ClO4)2·2H2O provides a suitable experimental platform of the antiferromagnetic spin-1 Heisenberg dimer, which allowed us to estimate a strength of the bipartite entanglement between two exchange-coupled Ni2+ magnetic ions on the grounds of the interaction constants reported previously from the fitting procedure of the magnetization data. It is verified that the negativity of this dinuclear compound is highly magnetic-field-orientation dependent due to presence of a relatively strong uniaxial single-ion anisotropy.