1,212
Views
61
CrossRef citations to date
0
Altmetric
Articles

Frontiers in frustrated magnetism

Pages 533-552 | Received 26 Jan 2009, Accepted 25 Feb 2009, Published online: 15 May 2009

References

  • One introduction to magnetism may be found in D.C. Mattis . 2006 . Theory of Magnetism Made Simple , Singapore : World Scientific . Ch. 1–5; and an introduction to local-moment magnetism and frustration in P. Fazekas, Lectures on Electron Correlation and Magnetism, World Scientific, Singapore, 1999, Ch. 1, 6
  • Läuchli , A. , Mila , F. and Penc , K. 2006 . The quadrupolar phases of the S = 1 bilinear-biquadratic Heisenberg model on the triangular lattice . Phys. Rev. Lett. , 97 : 087205
  • Read , N. and Sachdev , S. 1989 . Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets . Phys. Rev. Lett. , 62 : 1694 – 1697 .
  • Ng , K. -K. and Lee , T. -K. 2006 . Supersolid phase in spin dimer XXZ systems under magnetic field . Phys. Rev. Lett. , 97 : 127204
  • Sengupta , P. and Batista , C. D. 2007 . Spin supersolid in anisotropic spin-one Heisenberg chain . Phys. Rev. Lett. , 99 : 217205
  • Picon , J. -D. , Albuquerque , A. F. , Schmidt , K. P. , Laflorencie , N. , Troyer , M. and Mila , F. 2008 . Mechanisms for spin-supersolidity in S = 1/2 spin-dimer antiferromagnets . Phys. Rev. , B78 : 184418
  • Sengupta , P. and Batista , C. D. 2007 . Field-induced supersolid phase in spin-one Heisenberg models . Phys. Rev. Lett. , 98 : 227201
  • Fazekas , P. and Anderson , P. W. 1974 . On the ground-state properties of the anisotropic triangular antiferromagnet . Philos. Mag. , 30 : 423 – 440 .
  • Mermin , N. D. and Wagner , H. 1966 . Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models . Phys. Rev. Lett. , 17 : 1133 – 1136 .
  • Läuchli , A. , Schmid , G. and Troyer , M. 2003 . Phase diagram of a spin ladder with cyclic four-spin exchange . Phys. Rev. , B 67 : 100409(R)
  • Lacroix C. Mendels P. Mila F. Highly Frustrated Magnetism Springer Heidelberg 2009
  • Moessner , R. and Ramirez , A. P. 2006 . Geometrical frustration . Phys. Today , 59 : 24 – 29 . B. Goss Levi, New candidate emerges for a quantum spin liquid, Phys. Today 60 (2007), pp. 16–19
  • Diep H. T. Frustrated Spin Systems World Scientific Singapore 2004
  • Okamoto , Y. , Nohara , M. , Aruga-Katori , H. and Takagi , H. 2007 . Spin-liquid state in the S = 1/2 hyperkagome antiferromagnet Na4Ir3O8 . Phys. Rev. Lett. , 99 : 137207
  • Shores , M. P. , Nytko , E. A. , Barlett , B. M. and Nocera , D. G. 2005 . A structurally perfect S = 1/2 kagome antiferromagnet . J. Am. Chem. Soc. , 127 : 13462 – 13463 .
  • Wills , A. S. , Harrison , A. , Ritter , C. and Smith , R. I. 2000 . Magnetic properties of pure and diamagnetically doped jarosites: model kagome antiferromagnets with variable coverage of the magnetic lattice . Phys. Rev. , B 61 : 6156 – 6169 .
  • Keren , A. , Kojima , K. , Le , L. P. , Luke , G. M. , Wu , W. D. , Uemura , Y. J. , Takano , M. , Dabkowska , H. and Gingras , M. J.P. 1996 . Muon-spin-rotation measurements in the kagome lattice systems Cr-jarosite and Fe-jarosite . Phys. Rev. , B 53 : 6451 – 6454 .
  • Hiroi , Z. , Hanawa , M. , Kobayashi , N. , Nohara , M. , Takagi , H. , Kato , Y. and Takigawa , M. 2001 . Spin-1/2 kagome-like lattice in volborthite Cu3V2 O 7 (OH) 2 -H 2O . J. Phys. Soc. Jpn , 70 : 3377 – 3384 .
  • Obradors , X. , Labarta , A. , Isalgué , A. , Tejada , J. , Rodriguez , J. and Pernet , M. 1988 . Magnetic frustration and lattice dimensionality in SrCr8Ga4O19 . Solid State Commun. , 65 : 189 – 192 .
  • Hagemann , I. S. , Huang , Q. , Gao , X. P.A. , Ramirez , A. P. and Cava , R. J. 2001 . Geometric magnetic frustration in Ba2Sn2 Ga3ZnCr7O22: a two-dimensional spinel-based kagome lattice . Phys. Rev. Lett. , 86 : 894 – 897 .
  • A very large volume of research into the physical properties of ZnCu3(OH)6Cl2 has appeared in the last two years; references to the most recent experimental results may be found, for example in Dzyaloshinskii–Moriya anisotropy in the spin-1/2 kagome compound ZnCu3(OH)6Cl2 Zorko A. Nellutla S. van Tol J. Brunel L. C. Bert F. Duc F. Trombe J.-C. de Vries M. A. Harrison A. Mendels P. Phys. Rev. Lett. 2008 101 026405
  • Shimizu , Y. , Miyagawa , K. , Kanoda , K. , Maesato , M. and Saito , G. 2003 . Spin liquid state in an organic Mott insulator with a triangular lattice . Phys. Rev. Lett. , 91 : 107001
  • Kurosaki , Y. , Shimizu , Y. , Miyagawa , K. , Kanoda , K. and Saito , G. 2005 . Mott transition from a spin liquid to a Fermi liquid in the spin-frustrated organic conductor κ-(ET)2Cu2 (CN) 3 . Phys. Rev. Lett. , 95 : 177001
  • Rüegg , Ch. 2008 . Thermodynamics of the spin Luttinger liquid in a model ladder material . Phys. Rev. Lett. , 101 : 247202 and references therein
  • Bloch , I. , Dalibard , J. and Zwerger , W. 2008 . Many-body physics with ultracold gases . Rev. Mod. Phys. , 80 : 885 – 964 .
  • Santos , L. , Baranov , M. A. , Cirac , J. I. , Everts , H. -U. , Fehrmann , H. and Lewenstein , M. 2004 . Atomic quantum gases in kagome lattices . Phys. Rev. Lett. , 93 : 030601
  • Wu , C. , Bergmann , D. , Balents , L. and Das Sarma , S. 2007 . Flat bands and Wigner crystallization in the honeycomb optical lattice . Phys. Rev. Lett. , 99 : 070401
  • Hermele , M. , Senthil , T. and Fisher , M. P.A. 2005 . Algebraic spin liquid as the mother of many competing orders . Phys. Rev. , B 72 : 104404
  • Polyakov , A. M. 1977 . Quark confinement and topology of gauge theories . Nucl. Phys. , B 120 : 429 – 458 .
  • Hermele , M. , Senthil , T. , Fisher , M. P.A. , Lee , P. A. , Nagaosa , N. and Wen , X. -G. 2004 . On the stability of U(1) spin liquids in two dimensions . Phys. Rev. , B 70 : 214437
  • Majumdar , C. K. and Ghosh , D. K. 1969 . On Next-nearest-neighbor interaction in linear chain. I & II . J. Math. Phys. , 10 : 1388 – 1398 . ibid. 10 (1969), pp. 1399–1402
  • Bethe , H. 1931 . Zur Theorie der Metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette. (On the theory of metals. I. Eigenvalues and eigenfunctions of the linear atomic chain) . Z. Phys. , A 71 : 205 – 231 .
  • Fouet , J. -B. , Mambrini , M. , Sindzingre , P. and Lhuillier , C. 2003 . The planar pyrochlore: a valence-bond crystal . Phys. Rev. , B 67 : 054411
  • Mila , F. 1998 . Low-energy sector of the S = 1/2 kagome antiferromagnet . Phys. Rev. Lett. , 81 : 2356 – 2359 . M. Mambrini and F. Mila, RVB description of the low-energy singlets of the spin 1/2 kagome antiferromagnet. Eur. Phys. J. B 17 (2000), pp. 651–659
  • Liang , S. , Douçot , B. and Anderson , P. W. 1988 . Some new variational resonating-valence-bond-type wave functions for the spin-1/2 antiferromagnetic Heisenberg model on a square lattice . Phys. Rev. Lett. , 61 : 365 – 368 .
  • Hastings , M. B. 2004 . Lieb–Schultz–Mattis in higher dimensions . Phys. Rev. , B 69 : 104431
  • Nussinov , Z. , Batista , C. D. , Normand , B. and Trugman , S. A. 2007 . High-dimensional fractionalization and spinon deconfinement in pyrochlore antiferromagnets . Phys. Rev. , B 75 : 094411
  • Baxter , R. J. 1982 . Exactly Solved Models in Statistical Mechanics , London : Academic Press .
  • Ivanov , D. A. and Senthil , T. 2002 . Projected wave functions for fractionalized phases of quantum spin systems . Phys. Rev. , B 66 : 115111
  • Wen , X. -G. 1991 . Mean-field theory of spin-liquid states with finite energy gap and topological orders . Phys. Rev. , B 44 : 2664 – 2672 .
  • Ng , T.-K. , Zhou , Y. and Lang , L.-H. Topological glass states . preprint (2009), to appear in Europhys. Lett. Available at arXiv:0901.1736
  • Kitaev , A. and Preskill , J. 2006 . Topological entanglement entropy . Phys. Rev. Lett. , 96 : 110404 M. Levin and X.-G. Wen, Detecting topological order in a ground-state wave function, Phys. Rev. Lett. 96 (2006), 110405; Z. Nussinov and G. Ortiz, A symmetry principle for topological quantum order, 2007. Available at cond-mat/0702377
  • Dommange , S. , Mambrini , M. , Normand , B. and Mila , F. 2003 . Static impurities in the kagome lattice: dimer freezing and mutual repulsion . Phys. Rev. , B 68 : 224416
  • Levin , M. and Senthil , T. 2004 . Deconfined quantum criticality and Néet order via dimer disorder . Phys. Rev. , B 70 : 220403
  • Sachdev , S. and Vojta , M. Non-magnetic impurities as probes of insulating and doped Mott insulators in two dimensions . Proceedings of the XIII International Congress on Mathematical Physics . Edited by: Fokas , A. , Grigoryan , A. , Kibble , T. and Zegarlinski , B. Boston : International Press .
  • Roger , M. 1984 . Multiple exchange in 3He and in the Wigner solid . Phys. Rev. , B 30 : 6432 – 6457 . M. Roger, C. Bäuerle, Yu.M. Bunkov, A.-S. Chen, and H. Godfrin, Multiple-spin exchange on a triangular lattice: a quantitative interpretation of thermodynamic properties of two-dimensional solid 3He. Phys. Rev. Lett. 80 (1998), pp. 1308–1311
  • Misguich , G. , Lhuillier , C. , Bernu , B. and Waldtmann , C. 1999 . Spin-liquid phase of the multiple-spin exchange Hamiltonian on the triangular lattice . Phys. Rev. , B 60 : 1064 – 1074 . W. LiMing, G. Misguich, P. Sindzingre, and C. Lhuillier, From Néel long-range order to spin liquids in the multiple-spin exchange model. Phys. Rev. B 62 (2000), pp. 6372–6377
  • Coldea , R. , Hayden , S. M. , Aeppli , G. , Perring , T. G. , Frost , C. D. , Mason , T. E. , Cheong , S. -W. and Fisk , Z. 2001 . Spin waves and electronic interactions in La2CuO4 . Phys. Rev. Lett. , 86 : 5377 – 5380 . A.A. Katanin and A.P. Kampf, Theoretical analysis of magnetic Raman scattering in La 2 CuO 4 : two-magnon intensity with the inclusion of ring exchange. Phys. Rev. B 67 (2003), 100404(R)
  • Oleś , A. M. 2009 . Spin-orbital physics in transition-metal oxides . Acta Phys. Polonica , 115 : 36 – 46 .
  • Feiner , L. F. , Oleś , A. M. and Zaanen , J. 1997 . Quantum melting of magnetic order due to orbital fluctuations . Phys. Rev. Lett. , 78 : 2799 – 2802 . A. Reitsma, L.F. Feiner and A.M. Oleś, Orbital and spin physics in LiNiO 2 and NaNiO 2, New J. Phys. 7 (2005), 121
  • Khaliullin , G. 2005 . Orbital order and fluctuations in Mott insulators . Prog. Theor. Phys. Suppl. , 160 : 155 – 202 .
  • Normand , B. and Oleś , A. M. 2008 . Frustration and entanglement in the t2g spin–orbital model on a triangular lattice: valence–bond and generalized liquid states . Phys. Rev. , B 78 : 094427
  • Batista , C. D. and Trugman , S. A. 2004 . Exact ground states of a frustrated 2D magnet: deconfined fractional excitations at a first-order quantum phase transition . Phys. Rev. Lett. , 93 : 217202
  • Rokhsar , D. S. and Kivelson , S. A. 1988 . Superconductivity and the quantum hard-core dimer gas . Phys. Rev. Lett. , 61 : 2376 – 2379 .
  • Moessner , R. and Sondhi , S. 2001 . Resonating valence bond phase in the triangular-lattice quantum dimer model . Phys. Rev. Lett. , 86 : 1881 – 1884 .
  • Laughlin , R. B. 2002 . Fractional Quantization in Nobel Lectures, Physics 1996–2000 , Edited by: Ekspong , G. Singapore : World Scientific .
  • Capriotti , L. , Becca , F. , Parola , A. and Sorella , S. 2001 . Resonating valence bond wave functions for strongly frustrated spin systems . Phys. Rev. Lett. , 87 : 097201 A. Parola, S. Sorella, F. Becca, and L. Capriotti, The resonating valence bond wave functions in quantum antiferromagnets, 2005. Available at cond-mat/0502170
  • Sandvik , A. W. and Beach , K. S.D. 2007 . Monte Carlo simulations of quantum spin systems in the valence bond basis Available at arXiv:0704.1469
  • Yunoki , S. and Sorella , S. 2006 . Two spin liquid phases in the spatially anisotropic triangular Heisenberg model . Phys. Rev. , B 74 : 014408
  • Becca , F. , Capriotti , L. , Parola , A. and Sorella , S. 2007 . Exotic gapless spectrum induced by frustration in quantum antiferromagnets . Phys. Rev. , B 76 : 060401
  • Ran , Y. , Hermele , M. , Lee , P. A. and Wen , X. -G. 2007 . Projected wavefunction study of spin-1/2 Heisenberg model on the kagome lattice . Phys. Rev. Lett. , 98 : 117205
  • Hermele , M. , Ran , Y. , Lee , P. A. and Wen , X. -G. 2008 . Properties of an algebraic spin liquid on the kagome lattice . Phys. Rev. , B 77 : 224413
  • Levin , M. and Nave , C. P. 2007 . Tensor renormalization group approach to 2D classical lattice models . Phys. Rev. Lett. , 99 : 120601
  • Jiang , H. C. , Weng , Z. Y. and Xiang , T. 2008 . Accurate determination of tensor network state of quantum lattice models in two dimensions . Phys. Rev. Lett. , 101 : 090603
  • Jiang , H. C. , Xie , Z. Y. , Weng , Z. Y. and Xiang , T. 2008 . Second renormalization of tensor-network states Available at arXiv:0809.0182
  • Sandvik , A. W. and Vidal , G. 2007 . Variational quantum Monte Carlo simulations with tensor-network states . Phys. Rev. Lett. , 99 : 220602

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.