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Part B: Condensed Matter Physics

Two-dimensional quantum-spin-1/2 XXZ magnet in zero magnetic field: Global thermodynamics from renormalisation group theory

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Pages 1787-1824 | Received 09 Jul 2018, Accepted 20 Mar 2019, Published online: 17 Apr 2019

References

  • P.W. Anderson, The resonating valence bond state in La2CuO4 and superconductivity, Science 235 (1987), pp. 1196–1198.
  • T. Matsubara and H. Matsuda, A lattice model of liquid helium, I, Prog. Theor. Phys. 16 (1956), pp. 569–582.
  • H. Matsuda and T. Matsubara, A lattice model of liquid helium, II, Prog. Theor. Phys. 17 (1957), pp. 19–29.
  • N.D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17 (1966), pp. 1133–1136.
  • K. Yamaji and J. Kondo, On the high-temperature susceptibilities of the two-dimensional ferromagnetic Heisenberg spin systems, J. Phys. Soc. Jpn. 35 (1973), pp. 25–32.
  • M.E. Lines, Comparative studies of magnetism in KNiF3 and K2NiF4, Phys. Rev. 164 (1967), pp. 736–748.
  • J.A. Plascak, Quantum spin systems: Dynamical mean field renormalization group approach. J. Phys. A 17 (1984), pp. L697–L702.
  • S. Yunoki, Numerical study of the spin-flop transition in anisotropic spin-1/2 antiferromagnets, Phys. Rev. B 65 (2002), pp. 092402-1–092402-4.
  • S. Kar, K. Wierschem, and P. Sengupta, Magnons in a two-dimensional transverse-field XXZ model, Phys. Rev. B 96 (2017), pp. 045126-1–045126-11.
  • H.Q. Ding, Antiferromagnetic transitions in high-Tc materials, J. Phys.: Condens. Matter 2 (1990), pp. 7979–7984.
  • H.Q. Ding, Could in-plane exchange anisotropy induce the observed antiferromagnetic transitions in the undoped high-Tc materials?, Phys. Rev. Lett. 68 (1992), pp. 1927–1930.
  • H.D. Zhou, C. Xu, A.M. Hallas, H.J. Silverstein, C.R. Wiebe, I. Umegaki, J.Q. Yan, T.P. Murphy, J.H. Park, Y. Qiu, J.R.D. Copley, J.S. Gardner, and Y. Takano, Successive phase transitions and extended spin-excitation continuum in the S = 1/2 triangular-lattice antiferromagnet Ba3CoSb2% uppercaseo9, Phys. Rev. Lett. 109 (2012), pp. 267206-1–267206-5.
  • T. Susuki, N. Kurita, T. Tanaka, H. Nojiri, A. Matsuo, K. Kindo, and H. Tanaka, Magnetization process and collective excitations in the S=1/2 triangular-lattice Heisenberg antiferromagnet Ba3CoSb2O9, Phys. Rev. Lett. 110 (2013), pp. 267201-1–267201-5.
  • Y. Shirata, H. Tanaka, A. Matsuo, and K. Kindo, Experimental realization of a spin-1/2 triangular-lattice Heisenberg antiferromagnet, Phys. Rev. Lett. 108 (2012), pp. 057205-1–057205-5.
  • G. Koutroulakis, T. Zhou, Y. Kamiya, J.D. Thompson, H.D. Zhou, C.D. Batista, and S.E. Brown, Quantum phase diagram of the S=1/2 triangular-lattice antiferromagnet Ba3CoSb2% uppercaseo9, Phys. Rev. B 91 (2015), pp. 024410-1–024410-15.
  • G. Marmorini, D. Yamamoto, and I. Danshita, Umbrella-coplanar transition in the triangular XXZ model with arbitrary spin, Phys. Rev. B 93 (2016), pp. 224402-1–224402-8.
  • D. Yamamoto, G. Marmorini, and I. Danshita, Quantum phase diagram of the triangular-lattice xxz model in a magnetic field, Phys. Rev. Lett. 112 (2014), pp. 127203-1–1272031-5.
  • D. Yamamoto, G. Marmorini, and I. Danshita, Microscopic model calculations for the magnetization process of layered triangular-lattice quantum antiferromagnets. Phys. Rev. Lett. 114 (2015), pp. 027201-1–027201-5.
  • D. Yamamoto, H. Ueda, I. Danshita, G. Marmorini, T. Momoi, and T. Shimokawa, Exact diagonalization and cluster mean-field study of triangular-lattice XXZ antiferromagnets near saturation, Phys. Rev. B 96 (2017), pp. 014431-1–014431-12.
  • C.N. Yang and C.P. Yang, One-dimensional chain of anisotropic spin-spin interactions. I. Proof of Bethe's hypothesis for ground state in a finite system, Phys. Rev. 150 (1966), pp. 321–327.
  • R.G. Melko, A. Paramekanti, A.A. Burkov, A. Vishwanath, D.N. Sheng, and L. Balents, Supersolid order from disorder: Hard-core bosons on the triangular lattice, Phys. Rev. Lett. 95 (2005), pp. 127207-1–127207-4.
  • R.G. Melko, Simulations of quantum XXZ models on two-dimensional frustrated lattices, J. Phys.: Condens. Matter 19 (2007), pp. 145203-1–145203-10.
  • R.G. Melko, A. Del Maestro, and A.A. Burkov, Striped supersolid phase and the search for deconfined quantum criticality in hard-core bosons on the triangular lattice, Phys. Rev. B 74 (2006), pp. 214517-1–214517-9.
  • S.V. Isakov, S. Wessel, R.G. Melko, K. Sengupta, and Y.B. Kim, Hard-core bosons on the Kagome lattice: Valence-bond solids and their quantum melting, Phys. Rev. Lett. 97 (2006), pp. 147202-1–147202-4.
  • B. Sachs, T.O. Wehling, K.S. Novoselov, A.I. Lichtenstein, and M.I. Katsnelson, Ferromagnetic two-dimensional crystals: Single layers of K2CuF4, Phys. Rev. B 88 (2013), pp. 201402(R)-1–201402(R)-4.
  • Y. Ma, Y. Dai, M. Guo, C. Niu, Y. Zhu, and B. Huang, Evidence of the existence of magnetism in pristine VX2 monolayers (X  =  S, Se) and their strain-induced tunable magnetic properties, ACS Nano 6 (2012), pp. 1695–1701.
  • B.L. Chittari, Y. Park, D. Lee, M. Han, A.H. MacDonald, E. Hwang, and J. Jung, Electronic and magnetic properties of single-layer MPX3 metal phosphorous trichalcogenides, Phys. Rev. B 94 (2016), pp. 184428-1–184428-16.
  • J.U. Lee, S. Lee, J.H. Ryoo, S. Kang, T.Y. Kim, P. Kim, C.H. Park, J.G. Park, and H. Cheong, Ising-type magnetic ordering in atomically thin FePS3, Nano Lett. 16 (2016), pp. 7433–7438.
  • M.A. McGuire, H. Dixit, V.R. Cooper, and B.C. Sales, Coupling of crystal structure and magnetism in the layered, ferromagnetic insulator CrI3, Chem. Mater. 27 (2015), pp. 612–620.
  • J.L. Lado and J. Fernández-Rossier, On the origin of magnetic anisotropy in two dimensional CrI3, 2D Mater. 4 (2017), pp. 0350021–0350029.
  • M.S. Makivić and H.Q. Ding, Two-dimensional spin-1/2 Heisenberg antiferromagnet: A quantum Monte Carlo study, Phys. Rev. B 43 (1991), pp. 3562–3574.
  • E. Manousakis, The spin-1/2 Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides, Rev. Mod. Phys. 63 (1991), pp. 1–62.
  • T. Barnes, The 2d Heisenberg antiferromagnet in high-Tc superconductivity: A review of numerical techniques and results, Int. J. Mod. Phys. C 2 (1991), pp. 659–709.
  • S.S. Aplesnin, A study of anisotropic Heisenberg antiferromagnet with S = 1/2 on a square lattice by Monte-Carlo method, Phys. Status Solidi B 207 (1998), pp. 491–498.
  • K.W. Lee, C.E. Lee, and I.-m. Kim, Helicity modulus and vortex density in the two-dimensional easy-plane Heisenberg model on a square lattice, Solid State Commun. 135 (2005), pp. 95–98.
  • S. Whitlock, A.W. Glaetzle, and P. Hannaford, Simulating quantum spin models using Rydberg-excited atomic ensembles in magnetic microtrap arrays, J. Phys. B 50 (2017), pp. 074001-1–074001-13.
  • R. Toskovic, R. van den Berg, A. Spinelli, I.S. Eliens, B. van den Toorn, B. Bryant, J.S. Caux, and A.F. Otte, Atomic spin-chain realization of a model for quantum criticality, Nature Phys. 12 (2016), pp. 656–661.
  • P. Richerme, Z.X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A.V. Gorshkov, and C. Monroe, Non-local propagation of correlations in quantum systems with long-range interactions, Nature (London) 511 (2014), pp. 198–201.
  • P. Jurcevic, B.P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C.F. Roos, Quasiparticle engineering and entanglement propagation in a quantum many-body system, Nature (London) 511 (2014), pp. 202–205.
  • T. Graß, C. Muschik, A. Celi, R.W. Chhajlany, and M. Lewenstein, Synthetic magnetic fluxes and topological order in one-dimensional spin systems, Phys. Rev. A 91 (2015), pp. 063612-1–063612-8.
  • R. Nath, M. Dalmonte, A.W. Glaetzle, P. Zoller, F. Schmidt-Kaler, and R. Gerritsma, Hexagonal plaquette spin-spin interactions and quantum magnetism in a two-dimensional ion crystal, New J. Phys. 17 (2015), pp. 065018-1–065018-16.
  • T. Fukuhara, A. Kantian, M. Endres, M. Cheneau, P. Schauß, S. Hild, D. Bellem, U. Schollwöck, T. Giamarchi, C. Gross, I. Bloch, and S. Kuhr, Quantum dynamics of a mobile spin impurity, Nature Phys. 9 (2013), pp. 235–241.
  • T. Fukuhara, P. Schauß, M. Endres, S. Hild, M. Cheneau, I. Bloch, and C. Gross, Microscopic observation of magnon bound states and their dynamics, Nature (London) 502 (2013), pp. 76–79.
  • D. Loss and D.P. DiVincenzo, Quantum computation with quantum dots, Phys. Rev. A 57 (1998), pp. 120–126.
  • G. Burkard, D. Loss, and D.P. DiVincenzo, Coupled quantum dots as quantum gates, Phys. Rev. B59 (1999), pp. 2070–2078.
  • U. Glaser, H. Büttner, and H. Fehske, Entanglement and correlation in anisotropic quantum spin systems, Phys. Rev. A 68 (2003), pp. 032318-1–032318-8.
  • L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80 (2008), pp. 517–576.
  • M. Suzuki and H. Takano, Migdal renormalization group approach to quantum spin systems, Phys. Lett. 69A (1979), pp. 426–428.
  • H. Takano and M. Suzuki, Migdal-Kadanoff renormalization group approach to the spin-l/2 anisotropic Heisenberg model, J. Stat. Phys. 26 (1981), pp. 635–663.
  • O.S. Sarıyer, A.N. Berker, and M. Hinczewski, Excitation spectrum gap and spin-wave velocity of XXZ Heisenberg chains: Global renormalization-group calculation, Phys. Rev. B 77 (2008), pp. 134413-1–134413-10.
  • T. Tatsumi, Study of quantum spin 1/2 X-Y model by means of extended Migdal approximation, Prog. Theor. Phys. 65 (1981), pp. 451–462.
  • M. Barma, D. Kumar, and R.B. Pandey, Comment on ‘Migdal renormalization group approach to quantum spin systems’. J. Phys. C 12 (1979), pp. L909–L913.
  • C.N. Yang and C.P. Yang, Ground-state energy of a Heisenberg-Ising lattice, Phys. Rev. 147 (1966), pp. 303–306.
  • A.A. Migdal, Phase transitions in gauge and spin-lattice systems, Zh. Eksp. Teor. Fiz. 69 (1975), pp. 1457-–1465. [Sov. Phys. JETP 42 (1975), pp. 743–746], http://www.jetp.ac.ru/cgi-bin/e/index/e/42/4/p743?a = list
  • L.P. Kadanoff, Notes on Migdal's recursion formulas, Ann. Phys. (N.Y.) 100 (1976), pp. 359–394.
  • A.N. Berker and S. Ostlund, Renormalization-group calculations of finite systems: Order parameter and specific heat for epitaxial ordering. J. Phys. C 12 (1979), pp. 4961–4975.
  • M. Kaufman and R.B. Griffiths, Exactly soluble Ising models on hierarchical lattices, Phys. Rev. B24 (1981), pp. 496(R)–498(R).
  • R.B. Griffiths and M. Kaufman, Spin systems on hierarchical lattices. Introduction and thermodynamic limit, Phys. Rev. B 26 (1982), pp. 5022–5032.
  • M. Kaufman and R.B. Griffiths, Spin systems on hierarchical lattices. II. Some examples of soluble models, Phys. Rev. B 30 (1984), pp. 244–249.
  • A. Erbaş, A. Tuncer, B. Yücesoy, and A.N. Berker, Phase diagrams and crossover in spatially anisotropic d = 3 Ising, XY magnetic, and percolation systems: Exact renormalization-group solutions of hierarchical models, Phys. Rev. E 72 (2005), pp. 026129-1–026129-6.
  • K. Sano, I. Doi, and T. Minoguchi, The superfluid transition of4He in zeolite by the quantum lattice gas model, Jpn. J. Appl. Phys. 26 (1987), pp. 291–292.
  • I. Doi, The superfluid transition of4He adsorbed in zeolite —A theoretical study based on the quantum lattice gas model—, J. Phys. Soc. Jpn. 58 (1989), pp. 1312–1319.
  • S.A. Cannas, F.A. Tamarit, and C. Tsallis, A generalised Hubbard Hamiltonian: Influence of temperature and fractality, Solid State Commun. 78 (1991), pp. 685–690.
  • S.A. Cannas, F.A. Tamarit, and C. Tsallis, Generalized Hubbard Hamiltonian: Renormalization-group approach. Phys. Rev. B 45 (1992), pp. 10496–10508.
  • G. Migliorini and A.N. Berker, Finite-temperature phase diagram of the Hubbard model, Eur. Phys. J. B 17 (2000), pp. 3–6.
  • M. Hinczewski and A.N. Berker, Two superconducting phases in the d = 3 Hubbard model: Phase diagram and specific heat from renormalization-group calculations, Eur. Phys. J. B 48 (2005), pp. 1–17.
  • A. Falicov and A.N. Berker, Finite-temperature phase diagram of the t-J model: Renormalization-group theory, Phys. Rev. B 51 (1995), pp. 12458–12463.
  • M. Hinczewski and A.N. Berker, d = 3 anisotropic and d = 2 tJ models: Phase diagrams, thermodynamic properties, and chemical potential shift, Eur. Phys. J. B 51 (2006), pp. 461–472.
  • M. Hinczewski and A.N. Berker, Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using a d = 3 tJ model with quenched disorder, Phys. Rev. B 78 (2008), pp. 064507-1–064507-5.
  • C.N. Kaplan, A.N. Berker, and M. Hinczewski, Frustrated further-neighbor antiferromagnetic and electron-hopping interactions in the d = 3 t-J model: Finite-temperature global phase diagrams from renormalization group theory, Phys. Rev. B 80 (2009), pp. 214529-1–214529-11.
  • O.S. Sarıyer, M. Hinczewski, and A.N. Berker, Phase separation and charge-ordered phases of the d = 3 Falicov-Kimball model at nonzero temperature: Temperature-density-chemical potential global phase diagram from renormalization-group theory, Phys. Rev. B 84 (2011), pp. 205120-1–205120-13.
  • S.R. McKay and A.N. Berker, Magnetic susceptibilities of cluster-hierarchical models, Phys. Rev. B29 (1984), pp. 1315–1320.
  • R. Dekeyser, M. Reynaert, and M.H. Lee, Quantum renormalization for the anisotropic Heisenberg model, Physica (Utrecht) 86-88B (1977), pp. 627–628.
  • L. Onsager, Crystal statistics. I. A two-dimensional model with an order-disorder transition, Phys. Rev. 65 (1944), pp. 117–149.
  • M. Suzuki, Dependence of critical exponents upon symmetry, dimensionality, potential-range and strength of interaction, Phys. Lett. 38A (1972), pp. 23–24.
  • J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973), pp. 1181–1203.
  • J.M. Kosterlitz, The critical properties of the two-dimensional xy model, J. Phys. C 7 (1974), pp. 1046–1060.
  • J. Rogiers, E.W. Grundke, and D.D. Betts, The spin 1/2 XY model. III. Analysis of high temperature series expansions of some thermodynamic quantities in two dimensions, Can. J. Phys. 57 (1979), pp. 1719–1730.
  • D.J. Bishop and J.D. Reppy, Study of the superfluid transition in two-dimensional4 He films, Phys. Rev. Lett. 40 (1978), pp. 1727–1730.
  • A.F. Hebard and A.T. Fiory, Evidence for the Kosterlitz-Thouless transition in thin superconducting aluminum films, Phys. Rev. Lett. 44 (1980), pp. 291–294.
  • K. Epstein, A.M. Goldman, and A.M. Kadin, Vortex-antivortex pair dissociation in two-dimensional superconductors, Phys. Rev. Lett. 47 (1981), pp. 534–537.
  • D.J. Resnick, J.C. Garland, J.T. Boyd, S. Shoemaker, and R.S. Newrock, Kosterlitz-Thouless transition in proximity-coupled superconducting arrays, Phys. Rev. Lett. 47 (1981), pp. 1542–1545.
  • P. Martinoli and C. Leemann, Two dimensional Josephson junction arrays, J. Low Temp. Phys. 118 (2000), pp. 699–731.
  • Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier, and J. Dalibard, Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas, Nature (London) 441 (2006), pp. 1118–1121.
  • K.J. Strandburg, Two-dimensional melting, Rev. Mod. Phys. 60 (1988), pp. 161–207.
  • M. Suzuki, S. Miyashita, and A. Kuroda, Monte Carlo simulation of quantum spin systems. I, Prog. Theor. Phys. 58 (1977), pp. 1377–1387.
  • E. Loh, Jr, D.J. Scalapino, and P.M. Grant, Monte Carlo simulations of the quantum XXZ model in two dimensions, Physica Scripta 32 (1985), pp. 327–333.
  • E. Loh, Jr, D.J. Scalapino, and P.M. Grant, Monte Carlo studies of the quantum XY model in two dimensions, Phys. Rev. B 31 (1985), pp. 4712(R)–4714(R).
  • H.Q. Ding and M.S. Makivić, Kosterlitz-Thouless transition in the two-dimensional quantum XY model, Phys. Rev. B 42 (1990), pp. 6827(R)–6830(R).
  • H.Q. Ding, Phase transition and thermodynamics of quantum XY model in two dimensions, Phys. Rev. B 45 (1992), pp. 230–242.
  • L. Capriotti, A. Cuccoli, V. Tognetti, R. Vaia, and P. Verrucchi, Thermodynamics of two-dimensional XXZ easy-plane quantum Heisenberg magnets, J. Appl. Phys. 81 (1997), pp. 4137–4139.
  • A. Cuccoli, T. Roscilde, V. Tognetti, R. Vaia, and P. Verrucchi, Quantum Monte Carlo study of S=1/2 weakly anisotropic antiferromagnets on the square lattice, Phys. Rev. B 67 (2003), pp. 104414-1–104414-18.
  • B. Braiorr-Orrs, M. Weyrauch, and M.V. Rakov, Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models, Ukr. J. Phys. 61 (2016), pp. 613–626.
  • A. Cuccoli, T. Roscilde, V. Tognetti, R. Vaia, and P. Verrucchi, Phase transitions in two-dimensional anisotropic quantum magnets, Eur. Phys. J. B 20 (2001), pp. 55–64.
  • T. Roscilde, A. Cuccoli, and P. Verrucchi, Phase transitions in anisotropic two-dimensional quantum antiferromagnets, Phys. Status Solidi B 236 (2003), pp. 433–436.
  • J. Fröhlich and E.H. Lieb, Existence of phase transitions for anisotropic Heisenberg models, Phys. Rev. Lett. 38 (1977), pp. 440–442.
  • T. Kennedy, Long range order in the anisotropic quantum ferromagnetic Heisenberg model, Commun. Math. Phys. 100 (1985), pp. 447–462.
  • D.D. Betts, F.C. Salevsky, and J. Rogiers, Vortices in the two-dimensional s=1/2 XY model, J. Phys. A14 (1981), pp. 531–538.
  • J. Abouie, A. Langari, and M. Siahatgar, Thermodynamic behavior of the XXZ Heisenberg s=1/2 chain around the factorizing magnetic field, J. Phys.: Condens. Matter 22 (2010), pp. 216008-1–216008-7.
  • R.J. Liu and T.L. Chen, Variational cumulant expansion for the Heisenberg model with the critical temperature determined to third order, Phys. Rev. B 50 (1994), pp. 9169–9173.
  • J.R. de Sousa and I.P. Fittipaldi, Critical behavior of the anisotropic Heisenberg model by effective-field renormalization group, J. Appl. Phys. 75 (1994), pp. 5835–5837.
  • T. Ishikawa and T. Oguchi, Critical behavior of the spin system with anisotropic exchange interaction. II. Two-dimensional lattice, J. Phys. Soc. Jpn. 31 (1971), pp. 1021–1025.
  • T. Obokata, I. Ono, and T. Oguchi, Padé approximation to ferromagnet with anisotropic exchange interaction, J. Phys. Soc. Jpn. 23 (1967), pp. 516–521.
  • S. Hikami and T. Tsuneto, Phase transition of quasi-two dimensional planar system, Prog. Theor. Phys. 63 (1980), pp. 387–401.
  • C. Kawabata and A.R. Bishop, Monte Carlo simulation of the two-dimensional classical Heisenberg model with easy-plane anisotropy, Solid State Commun. 42 (1982), pp. 595–600.
  • A. Cuccoli, V. Tognetti, P. Verrucchi, and R. Vaia, The quantum 2-D XXZ ferromagnet, J. Magn. Magn. Mater. 140-144 (1995), pp. 1703–1704.
  • B. Vogt and S. Kettemann, Reduction of quantum fluctuations by anisotropy fields in Heisenberg ferro- and antiferromagnets, Ann. Phys. (Berlin) 18 (2009), pp. 759–782.
  • C.N. Kaplan and A.N. Berker, Quantum-mechanically induced asymmetry in the phase diagrams of spin-glass systems, Phys. Rev. Lett. 100 (2008), pp. 027204-1–027204-4.
  • J. Oitmaa and W. Zheng, Curie and Néel temperatures of quantum magnets, J. Phys.: Condens. Matter 16 (2004), pp. 8653–8660.
  • G.S. Rushbrooke and P.J. Wood, On the high temperature staggered susceptibility of Heisenberg model antiferromagnetics, Mol. Phys. 6 (1963), pp. 409–421.
  • H.K. Charles, Jr and R.I. Joseph, Critical properties of antiferromagnets, Phys. Rev. Lett. 28 (1972), pp. 823–825.
  • P.W. Kasteleijn, J. Van Kranendonk, Constant coupling approximation for Heisenberg ferromagnetism, Physica (Utrecht) 22 (1956), pp. 317–337.
  • P.W. Kasteleijn, J. Van Kranendonk, Constant coupling approximation for antiferromagnetism, Physica (Utrecht) 22 (1956), pp. 367–385.
  • H. Mano, Study of critical phenomena of quantum spin systems by spin-cluster approximation series, J. Magn. Magn. Mater. 90-91 (1990), pp. 281–283.
  • J. Oitmaa and D.D. Betts, The ground state of two quantum models of magnetism, Can. J. Phys.56 (1978), pp. 897–901.
  • K. Kubo and T. Kishi, Existence of long-range order in the XXZ model, Phys. Rev. Lett. 61 (1988), pp. 2585–2587.
  • Y. Ozeki, H. Nishimori, and Y. Tomita, Long-range order in antiferromagnetic quantum spin systems, J. Phys. Soc. Jpn. 58 (1989), pp. 82–90.
  • H. Nishimori and Y. Ozeki, Ground-state long-range order in the two-dimensional XXZ model, J. Phys. Soc. Jpn. 58 (1989), pp. 1027–1030.
  • H.A. Wischmann and E. Müller-Hartmann, Extended proof of long-range order in the two-dimensional quantum spin-1/2 XXZ-model at T = 0, J. Phys. I (Paris) 1 (1991), pp. 647–657.
  • T. Kennedy, E.H. Lieb, and B.S. Shastry, The XY model has long-range order for all spins and all dimensions greater than one, Phys. Rev. Lett. 61 (1988), pp. 2582–2584.
  • S. Takada, A path-integral approach to the X-Y model in one- and two-dimensions, Prog. Theor. Phys. 63 (1980), pp. 1121–1136.
  • T. Roscilde, P. Verrucchi, A. Fubini, S. Haas, and V. Tognetti, Studying quantum spin systems through entanglement estimators, Phys. Rev. Lett. 93 (2004), pp. 167203-1–167203-4.
  • W.K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80 (1998), pp. 2245–2248.
  • F.F. Fanchini, T. Werlang, C.A. Brasil, L.G.E. Arruda, and A.O. Caldeira, Non-Markovian dynamics of quantum discord, Phys. Rev. A 81 (2010), pp. 052107-1–052107-6.
  • T. Werlang, C. Trippe, G.A.P. Ribeiro, and G. Rigolin, Quantum correlations in spin chains at finite temperatures and quantum phase transitions, Phys. Rev. Lett. 105 (2010), pp. 095702-1–095702-4.
  • L. Justino and T.R. de Oliveira, Bell inequalities and entanglement at quantum phase transitions in the XXZ model, Phys. Rev. A 85 (2012), pp. 052128-1–052128-7.
  • H. Ollivier and W.H. Zurek, Quantum discord: A measure of the quantumness of correlations, Phys. Rev. Lett. 88 (2001), pp. 017901-1–017901-4.
  • S. Luo, Quantum discord for two-qubit systems, Phys. Rev. A 77 (2008), pp. 042303-1–042303-6.
  • L. Balents, Spin liquids in frustrated magnets, Nature (London) 464 (2010), pp. 199–208.
  • S. Hirata, N. Kurita, M. Yamada, and H. Tanaka, Quasi-two-dimensional Bose-Einstein condensation of lattice bosons in the spin-1/2 XXZ ferromagnet K2CuF4, Phys. Rev. B 95 (2017), pp. 174406-1–174406-5.
  • J.S. Helton, K. Matan, M.P. Shores, E.A. Nytko, B.M. Bartlett, Y. Yoshida, Y. Takano, A. Suslov, Y. Qiu, J.H. Chung, D.G. Nocera, and Y.S. Lee, Spin dynamics of the spin-1/2 Kagome lattice antiferromagnet ZnCu3(OH)6Cl2, Phys. Rev. Lett. 98 (2007), pp. 107204-1–107204-4.
  • T. Han, S. Chu, and Y.S. Lee, Refining the spin Hamiltonian in the spin-1/2 Kagome lattice antiferromagnet ZnCu3(OH)6Cl2 using single crystals, Phys. Rev. Lett. 108 (2012), pp. 157202-1–157202-5.
  • V.S. Viswanath, S. Zhang, J. Stolze, and G. Müller, Ordering and fluctuations in the ground state of the one-dimensional and two-dimensional S=1/2 XXZ antiferromagnets: A study of dynamical properties based on the recursion method, Phys. Rev. B 49 (1994), pp. 9702–9715.
  • M.S. Sarandy, Classical correlation and quantum discord in critical systems, Phys. Rev. A 80 (2009), pp. 022108-1–022108-9.
  • R.F. Bishop, D.J.J. Farnell, and J.B. Parkinson, The coupled-cluster method applied to the XXZ model using a planar model state, J. Phys.: Condens. Matter 8 (1996), pp. 11153–11165.
  • W.L. You and Y.L. Dong, Fidelity susceptibility in two-dimensional spin-orbit models, Phys. Rev. B84 (2011), pp. 174426-1–174426-10.
  • H.Q. Lin, J.S. Flynn, and D.D. Betts, Exact diagonalization and quantum Monte Carlo study of the spin-1/2 XXZ model on the square lattice, Phys. Rev. B 64 (2001), pp. 214411-1–214411-9.
  • S.J. Gu, G.S. Tian, and H.Q. Lin, Ground-state entanglement in the XXZ model, Phys. Rev. A 71 (2005), pp. 052322-1–052322-5.
  • R. Dillenschneider, Quantum discord and quantum phase transition in spin chains, Phys. Rev. B 78 (2008), pp. 224413-1–224413-7.
  • W.Y. Sun, J.D. Shi, D. Wang, and L. Ye, Exploring the global entanglement and quantum phase transition in the spin 1/2 xxz model with dzyaloshinskii-moriya interaction, Quantum Inf. Process.15 (2016), pp. 245–253.
  • W.Y. Sun, S. Xu, C.C. Liu, and L. Ye, Negativity and quantum phase transition in the spin model using the quantum renormalization-group method, Int. J. Theor. Phys. 55 (2016), pp. 2548–2557.
  • W.Y. Sun, D. Wang, J.D. Shi, and L. Ye, Exploration quantum steering, nonlocality and entanglement of two-qubit x-state in structured reservoirs, Sci. Rep. 7 (2017), pp. 39651.
  • W.Y. Sun, D. Wang, and L. Ye, Various quantum measures and quantum phase transition within one-dimensional anisotropic spin-1/2 heisenberg xxz model, Physica B 524 (2017), pp. 27–33.
  • C.C. Liu, D. Wang, W.Y. Sun, and L. Ye, Quantum coherence, uncertainty, nonlocal advantage of quantum coherence as indicators of quantum phase transition in the transverse ising model, Laser Phys. Lett. 14 (2017), pp. 105202.
  • M. Suzuki and S. Miyashita, Variational study on the ground state of the spin-1/2 XY magnet, Can. J. Phys. 56 (1978), pp. 902–912.
  • M. Al Hajj, N. Guihéry, J.P. Malrieu, and P. Wind, Theoretical studies of the phase transition in the anisotropic two-dimensional square spin lattice, Phys. Rev. B 70 (2004), pp. 094415-1–094415-6.
  • K.A. Penson, R. Jullien, and P. Pfeuty, Zero-temperature renormalization-group method for quantum systems. IV. S=1/2 XY model in a transverse field in two and three dimensions, Phys. Rev. B 22 (1980), pp. 380–394.
  • D.D. Betts, Critical properties of the XY model, Physica (Utrecht) 86-88B (1977), pp. 556–561.
  • D.D. Betts, H.Q. Lin, and J.S. Flynn, Improved finite-lattice estimates of the properties of two quantum spin models on the infinite square lattice, Can. J. Phys. 77 (1999), pp. 353–369.
  • R.B. Pearson, Estimates of the ground-state eigenvalue of the two-dimensional spin-1/2 X-Y model, Phys. Rev. B 16 (1977), pp. 1109–1111.

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