Quantum phase transitions in spin-1 XXZ chains with rhombic single-ion anisotropy

Abstract

We explore numerically the inverse participation ratios in the ground-state of one-dimensional spin-1 XXZ 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 Y-Néel phase to the large-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 ∆ and the rhombic single-ion anisotropy E.

Determining the anisotropy and exchange parameters of polycrystalline spin-1 magnets

“…Thus the uniform g approximation is reasonable within the errors of the thermodynamic measurements. The parameters resulting from the fit to 16 χ(T) are g=2.24 (1), an easy-plane D=8.7(2) K, E=1.2(2) K and χ 0 =−8(1)×10 −9 m 3 mol −1 .…”

“…We will apply the analysis to three new materials in which Ni(II) ions are separated from one another by organic ligands. These are (1) [Ni(H 2 O) 2 (3,5-lutidine) 4 ](BF 4 ) 2 and (2) Ni(H 2 O) 2 (acetate) 2 (4-picoline) 2 , both of which we find to be dominated by single-ion anisotropy with no evidence of a significant role for exchange interactions at the temperatures measured, and (3) the antiferromagnet [Ni(H 2 O) 2 (pyrazine) 2 ](BF 4 ) 2 . System (1) was designed to have NiN 4 O 2 octahedra similar to that of (3), but without extended interaction pathways, such that the effect of the local environment on the anisotropy could be elucidated in the absence of exchange, and we will discuss to what extent this approach has been successful.…”

“…Of particular relevance here are quasi-one-dimensional and quasi-two-dimensional systems based on S=1 magnetic moments, which inspire a great deal of contemporary theoretical attention (e.g. [1][2][3][4][5][6][7][8]) and are predicted to display vibrant phase diagrams arising from competing interactions and their interplay with singleion anisotropy. These diagrams encompass quantum critical points [1,2], nematic and supersolid states [5,9,10], as well as topologically interesting gapped and quantum paramagnetic phases [11][12][13][14].…”

Quantum phase transitions in a spin-1 antiferromagnetic chain with long-range interactions and modulated single-ion anisotropy

“…Anisotropy effects can then significantly modify the ground state magnetic properties. A sufficiently strong easy plane single-ion anisotropy ∝ D(S z i ) 2 induces a Gaussian quantum phase transition (QPT) with central charge c = 1 from the SPT state to a topologically trivial large-D phase [19][20][21][22][23][24][25] [cf. Fig.…”

Phase Diagram of the Spin-1/2 Heisenberg Alternating Chain in a Magnetic Field*

“…Fortunately, with the development of quantum information, various information measures, e.g., quantum coherence, entanglement entropy, and fidelity, can help us to study quantum critical phenomena in spin chains. It is found that the quantum critical points can be well characterized by both the ground-state entanglement and fidelity on large system [27][28][29][30][31][32][33][34]. In this paper we study the entanglement, coherence and fidelity of the spin-1/2 Heisenberg alternating chain under a transverse magnetic field, and finally the phase diagram will be given.…”