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Journal of Materials Science

, Volume 55, Issue 6, pp 2257–2290 | Cite as

Theoretical and experimental developments in quantum spin liquid in geometrically frustrated magnets: a review

  • V. R. ShaginyanEmail author
  • V. A. Stephanovich
  • A. Z. Msezane
  • G. S. Japaridze
  • J. W. Clark
  • M. Ya. Amusia
  • E. V. Kirichenko
Review
  • 148 Downloads

Abstract

The exotic substances have exotic properties. One class of such substances is geometrically frustrated magnets, where correlated spins reside in the sites of triangular or kagomé lattice. In some cases, such magnet would not have long-range magnetic order. Rather, its spins tend to form kind of pairs, called valence bonds. At \(T \rightarrow 0\) these highly entangled quantum objects condense in the form of a liquid, called quantum spin liquid (QSL). The observation of a gapless QSL in actual materials is of fundamental significance both theoretically and technologically, as it could open a path to creation of topologically protected states for quantum information processing and computation. In the present review, we consider QSL formed by spinons that are chargeless fermionic quasiparticles with spin 1/2, filling the Fermi sphere up to the Fermi momentum \(p_{\rm F}\). We expose a state of the art in the theoretical and experimental investigations of the thermodynamic, relaxation, transport, optical and scaling properties of geometrically frustrated magnets with QSL. We show how different theoretical approaches and that based on so-called fermion condensation concept among them, permit to describe the multitude of experimental results regarding the thermodynamic and transport properties of QSL in geometrically frustrated magnets like herbertsmithite \(\hbox {ZnCu}_3(\hbox {OH})_6\hbox {Cl}_2\), the organic insulators \(\hbox {EtMe}_3\hbox {Sb}[\hbox {Pd(dmit)}_2]_2\) and \(\kappa {\text {-}}(\hbox {BEDT-TTF})_2\hbox {Cu}_2(\hbox {CN})_3\), quasi-one-dimensional spin liquid in the \(\hbox {Cu}(\hbox {C}_4\hbox {H}_4\hbox {N}_2)(\hbox {NO}_3)_2\) insulator and QSL formed in two-dimensional \(^3\hbox {He}\). Our theoretical results are in good agreement with experimental facts, while predictions, elucidating the existence of gapless QSL in magnets, still await their experimental confirmation.

Notes

Acknowledgements

This work is supported by the National Science Center in Poland as a research project No. DEC-2017/27/B/ST3/02881. This work was partly supported by U.S. DOE, Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research. JWC is indebted to the University of Madeira and its Centro de Ciéncias Matemáticas for gracious hospitality during his sabbatical residency.

References

  1. 1.
    Binder K, Young AP (1986) Spin glasses: eperimental facts, theoretical concepts, and open questions. Rev Mod Phys 58:801–976CrossRefGoogle Scholar
  2. 2.
    Mézard M, Parisi G, Virasoro MA (2004) Spin glass theory and beyond. World scientific lecture notes in physics 9Google Scholar
  3. 3.
    Khodel VA, Shaginyan VR (1990) Superfluidity in system with fermion condensate. JETP Lett 51:553–555Google Scholar
  4. 4.
    Khodel VA, Shaginyan VR, Khodel VV (1994) New approach in the microscopic Fermi systems theory. Phys Rep 249:1–134CrossRefGoogle Scholar
  5. 5.
    Shaginyan VR, Amusia M Ya, Popov KG (2007) Universal behavior of strongly correlated Fermi systems. Phys Usp 50:563–593CrossRefGoogle Scholar
  6. 6.
    Shaginyan VR, Amusia M Ya, Msezane AZ, Popov KG (2010) Scaling behavior of heavy fermion metals. Phys Rep 492:31–109CrossRefGoogle Scholar
  7. 7.
    Shaginyan VR, Popov KG, Khodel VA (2014) Conventional BCS, unconventional BCS, and non-BCS hidden dineutron phases in neutron matter. Phys Atomic Nucl 77:1063–1078CrossRefGoogle Scholar
  8. 8.
    Amusia M Ya, Popov KG, Shaginyan VR, Stephanovich VA (2014) Theory of heavy-fermion compounds. Springer series in solid-state sciences 182Google Scholar
  9. 9.
    Balents L (2010) Spin liquids in frustrated magnets. Nature 464:199–208CrossRefGoogle Scholar
  10. 10.
    Schrödinger E (1935) Die gegenwärtige situation in der quantenmechanik. Naturwissenschaften 23:807–812CrossRefGoogle Scholar
  11. 11.
    Verstraete F, Martín-Delgado MA, Cirac JI (2004) Diverging entanglement length in gapped quantum spin systems. Phys Rev Lett 92:087201CrossRefGoogle Scholar
  12. 12.
    Bennett CH, DiVincenzo DP (2000) Quantum information and computation. Nature 404:247–255CrossRefGoogle Scholar
  13. 13.
    Gühne O, Tóth G (2009) Entanglement detection. Phys Rep 474:1–76CrossRefGoogle Scholar
  14. 14.
    Nikuni T, Oshikawa M, Oosawa A, Tanaka H (2000) Bose–Einstein condensation of dilute magnons in \(\rm {TlCuCl}_3\). Phys Rev Lett 84:5868–5871CrossRefGoogle Scholar
  15. 15.
    Affleck I, Kennedy T, Lieb EH, Tasaki H (1987) Rigorous results on valence-bond ground states in antiferromagnets. Phys Rev Lett 59:799–802CrossRefGoogle Scholar
  16. 16.
    Anderson PW (1973) Resonating valence bonds: a new kind of insulator? Mater Res Bull 8:153–160CrossRefGoogle Scholar
  17. 17.
    Balents L, Fisher MPA, Girvin SM (2002) Fractionalization in an easy-axis Kagomé antiferromagnet. Phys Rev B 65:224412CrossRefGoogle Scholar
  18. 18.
    Kitaev A (2006) Anyons in an exactly solved model and beyond. Ann Phys (Leipzig) 321:2–111CrossRefGoogle Scholar
  19. 19.
    Moessner R, Sondhi SL (2001) Resonating valence bond phase in the triangular lattice quantum dimer model. Phys Rev Lett 86:1881–1884CrossRefGoogle Scholar
  20. 20.
    Irkhin VYu, Katanin AA, Katsnelson MI (2002) Robustness of the Van Hove scenario for high-\(T_{\rm c}\) superconductors. Phys Rev Lett 89:076401CrossRefGoogle Scholar
  21. 21.
    Yudin D, Hirschmeier D, Hafermann H, Eriksson O, Lichtenstein AI, Katsnelson MI (2014) Fermi condensation near van hove singularities within the hubbard model on the triangular lattice. Phys Rev Lett 112:070403CrossRefGoogle Scholar
  22. 22.
    Vojta M (2018) Frustration and quantum criticality. Rep Prog Phys 81:064501CrossRefGoogle Scholar
  23. 23.
    Irkhin VYu (2017) Unconventional magnetism of the Kondo Lattice. Phys Usp 60:747–761CrossRefGoogle Scholar
  24. 24.
    Bergman DL, Wu C, Balents L (2008) Band touching from real-space topology in frustrated hopping models. Phys Rev B 78:125104CrossRefGoogle Scholar
  25. 25.
    Green D, Santoz L, Chamon C (2010) Isolated flat bands and spin-1 conical bands in two-dimensional lattices. Phys Rev B 82:075104CrossRefGoogle Scholar
  26. 26.
    Shaginyan VR, Msezane AZ, Popov KG (2011) Thermodynamic properties of the kagomé lattice in herbertsmithite. Phys Rev B 84:060401(R)CrossRefGoogle Scholar
  27. 27.
    Shaginyan VR, Msezane AZ, Popov KG, Khodel VA (2012) Scaling in dynamic susceptibility of herbertsmithite and heavy-fermion metals. Phys Lett A 376:2622–2626CrossRefGoogle Scholar
  28. 28.
    Shaginyan VR, Msezane AZ, Popov KG, Japaridze GS, Stephanovich VA (2012) Identification of strongly correlated spin liquid in herbertsmithite. Europhys Lett 97:56001CrossRefGoogle Scholar
  29. 29.
    Shaginyan VR, Msezane AZ, Popov KG, Japaridze GS, Khodel VA (2013) Heat transport in magnetic fields by quantum spin liquid in the organic insulators \(\text{EtMe}_3\text{Sb}[\text{Pd(dmit)}_2]_2\) and \(\kappa{\hbox{-}}(\text{BEDT-TTF})_2\text{Cu}_2(\text{CN})_3\). Europhys Lett 103:67006CrossRefGoogle Scholar
  30. 30.
    Changlani HJ, Kochkov D, Kumar K, Clark BK, Fradkin E (2018) Macroscopically degenerate exactly solvable point in the spin-1/2 kagomé quantum antiferromagnet. Phys Rev Lett 120:117202CrossRefGoogle Scholar
  31. 31.
    Lambor JL, Dutrizac JE, Roberts AC, Grice JD, Szymanski JT (1996) Clinoatacamite, a new polymorph of \(\text{Cu}_2(\text{OH})_3\text{Cl}\), and its relationship to paratacamite and “anarakite”. Can Mineral 34:61–72Google Scholar
  32. 32.
    Shores MP, Nytko EA, Bartlett BM, Nocera DG (2005) A structurally perfect S = 1/2 kagomé antiferromagnet. J Am Chem Soc 127:13462–13463CrossRefGoogle Scholar
  33. 33.
    Helton JS, Matan K, Shores MP, Nytko EA, Bartlett BM, Qiu Y, Nocera DG, Lee YS (2010) Dynamic scaling in the susceptibility of the spin-1/2 kagomé lattice antiferromagnet herbertsmithite. Phys Rev Lett 104:147201CrossRefGoogle Scholar
  34. 34.
    Helton JS, Matan K, Shores MP, Nytko EA, Bartlett BM, Yoshida Y, Takano Y, Suslov A, Qiu Y, Chung J-H, Nocera DG, Lee YS (2007) Spin dynamics of the spin-1/2 kagomé lattice antiferromagnet \(\text{ZnCu}_3(\text{OH})_6\text{Cl}_2\). Phys Rev Lett 98:107204CrossRefGoogle Scholar
  35. 35.
    deVries MA, Kamenev KV, Kockelmann WA, Sanchez-Benitez J, Harrison A (2008) Magnetic ground state of an experimental \(S=1/2\) kagomé antiferromagnet. Phys Rev Lett 100:157205CrossRefGoogle Scholar
  36. 36.
    Han TH, Helton JS, Chu S, Prodi A, Singh DK, Mazzoli C, Müller P, Nocera DG, Lee YS (2011) Synthesis and characterization of single crystals of the spin-1/2 kagomé-lattice antiferromagnets \(\text{Zn}_{x}\text{Cu}_{4-{x}}(\text{OH})_6{\rm Cl}_2\). Phys Rev B 83:100402(R)CrossRefGoogle Scholar
  37. 37.
    Han TH, Chu S, Lee YS (2012) Refining the spin hamiltonian in the spin-1/2 kagomé lattice antiferromagnet \(\text{ZnCu}_3(\text{OH})_6\text{Cl}_2\) using single crystals. Phys Rev Lett 108:157202CrossRefGoogle Scholar
  38. 38.
    Han TH, Chisnell R, Bonnoit CJ, Freedman DE, Zapf VS, Harrison N, Nocera DG, Takano Y, Lee YS (2014) Thermodynamic properties of the quantum spin liquid candidate \(\text{ZnCu}_3(\text{OH})_6\text{C}_2\) in high magnetic fields. arXiv:1402.2693
  39. 39.
    Liao HJ, Xie ZY, Chen J, Liu ZY, Xie HD, Huang RZ, Normand B, Xiang T (2017) Gapless spin-liquid ground state in the S = 1/2 kagomé antiferromagnet. Phys Rev Lett 118:137202CrossRefGoogle Scholar
  40. 40.
    Shaginyan VR, Amusia M Ya, Msezane AZ, Popov KG, Stephanovich VA (2015) Heavy fermion spin liquid in herbertsmithite. Phys Lett A 379:2092–2096CrossRefGoogle Scholar
  41. 41.
    Norman MR (2016) Herbertsmithite and the search for the quantum spin liquid. Rev Mod Phys 88:041002CrossRefGoogle Scholar
  42. 42.
    Mendels P, Bert F (2016) Quantum kagomé frustrated antiferromagnets: one route to quantum spin liquids. C R Phys 17:455–470CrossRefGoogle Scholar
  43. 43.
    Zhou Yi, Kanoda K, Ng T-K (2017) Quantum spin liquid states. Rev Mod Phys 89:025003CrossRefGoogle Scholar
  44. 44.
    Han TH, Norman MR, Wen J-J, Rodriguez-Rivera JA, Helton JS, Broholm C, Lee YS (2016) Correlated impurities and intrinsic spin-liquid physics in the kagomé material herbertsmithite. Phys Rev B 94:060409(R)CrossRefGoogle Scholar
  45. 45.
    Savary L, Balents L (2017) Quantum spin liquids: a review. Rep Prog Phys 80:016502CrossRefGoogle Scholar
  46. 46.
    Hickey C, Trebst S (2019) Emergence of a field-driven U(1) spin liquid in the Kitaev honeycomb mode. Nat Commun 10:530CrossRefGoogle Scholar
  47. 47.
    Jackeli G, Khaliullin G (2009) Mott insulators in the strong spin-orbit coupling limit: from Heisenberg to a quantum compass and Kitaev models. Phys Rev Lett 102:017205CrossRefGoogle Scholar
  48. 48.
    Majorana E (1937) Teoria simmetrica dell’elettrone e del positrone. Il Nuovo Cimento 14:171–184CrossRefGoogle Scholar
  49. 49.
    Ran Y, Hermele M, Lee PA, Wen X-G (2007) Projected-wave-function study of the spin-1/2 Heisenberg model on the kagomé lattice. Phys Rev Lett 98:117205CrossRefGoogle Scholar
  50. 50.
    Hastings MB (2000) Dirac structure, RVB, and Goldstone modes in the kagomé antiferromagnet. Phys Rev B 63:014413CrossRefGoogle Scholar
  51. 51.
    Baskaran G, Zou Z, Anderson PW (1987) The resonating valence bond state and high-\(T_{\rm c}\) superconductivity: a mean field theory. Solid State Commun 63:973–976CrossRefGoogle Scholar
  52. 52.
    Iqbal Y, Hu W-J, Thomale R, Poilblanc D, Becca F (2016) Spin liquid nature in the Heisenberg \(J_1- J_2\) triangular antiferromagnet. Phys Rev B 93:144411CrossRefGoogle Scholar
  53. 53.
    He Y-C, Zaletel MP, Oshikawa M, Pollmann F (2017) Signatures of dirac cones in a DMRG study of the kagomé Heisenberg model. Phys Rev X 7:031020Google Scholar
  54. 54.
    Potter AC, Senthil T, Lee PA (2013) Mechanisms for sub-gap optical conductivity in Herbertsmithite. Phys Rev B 87:245106CrossRefGoogle Scholar
  55. 55.
    Newns DM, Read N (1987) Mean-field theory of intermediate valence/heavy fermion systems. Adv Phys 36:799CrossRefGoogle Scholar
  56. 56.
    Lifshits EM, Pitaevsky LP (2014) Statistical physics, part 2. Butterworth-Heinemann, OxfordGoogle Scholar
  57. 57.
    Landau LD (1956) The theory of a Fermi liquid. Sov Phys JETP 3:920–925Google Scholar
  58. 58.
    Pines D, Noziéres P (1966) Theory of quantum liquids. Benjamin, New YorkGoogle Scholar
  59. 59.
    Volovik GE (1991) A new class of normal Fermi liquids. JETP Lett 53:222–225Google Scholar
  60. 60.
    Volovik GE (2007) Quantum phase transitions from topology in momentum space. Lect Notes Phys 718:31–73CrossRefGoogle Scholar
  61. 61.
    Shaginyan VR, Stephanovich VA, Msezane AZ, Schuck P, Clark JW, Amusia M Ya, Japaridze GS, Popov KG, Kirichenko EV (2017) New state of matter: heavy fermion systems, quantum spin liquids, quasicrystals, cold gases, and high-temperature superconductors. J Low Temp Phys 189:410–450CrossRefGoogle Scholar
  62. 62.
    Nozières P (1992) Properties of Fermi liquids with a finite range interaction. J Phys I France 2:443–458CrossRefGoogle Scholar
  63. 63.
    Shaginyan VR, Stephanovich VA, Popov KG, Kirichenko EV, Artamonov SA (2016) Magnetic quantum criticality in quasi-one-dimensional Heisenberg antiferromagnet \(\text{Cu}(\text{C}_4\text{H}_4\text{N}_2)(\text{NO}_3)_2\). Ann Phys (Berlin) 528:483–492CrossRefGoogle Scholar
  64. 64.
    Isono T, Terashima T, Miyagawa K, Kanoda K, Uji S (2016) Quantum criticality in an organic spin-liquid insulator \(\kappa{\hbox{-}}(\text{BEDT-TTF})_2\text{Cu}_2(\text{CN})_3\). Nat Commun 7:13494.  https://doi.org/10.1038/ncomms13494 CrossRefGoogle Scholar
  65. 65.
    Isono T, Sugiura S, Terashima T, Miyagawa K, Kanoda K, Uji S (2018) Spin-lattice decoupling in a triangular-lattice quantum spin liquid. Nat Commuun 9:1509.  https://doi.org/10.1038/s41467-018-04005-1 CrossRefGoogle Scholar
  66. 66.
    Farmer WM, Skinner SF, ter Haarb LW (2018) Heat capacity of the highly frustrated triangulated kagomé lattice \(\text{Cu}_9\text{Cl}_2(\text{cpa})_6\). AIP Adv 8:101404CrossRefGoogle Scholar
  67. 67.
    Imai T, Fu M, Han TH, Lee YS (2011) Local spin susceptibility of the S=1/2 kagomé lattice in \(\text{ZnCu}_3(\text{OD})_6\text{Cl}_2\). Phys Rev B 84:020411(R)CrossRefGoogle Scholar
  68. 68.
    Fu M, Imai T, Han TH, Lee YS (2015) Evidence for a gapped spin-liquid ground state in a kagomé Heisenberg antiferromagnet. Science 350:655–658CrossRefGoogle Scholar
  69. 69.
    Gegenwart P, Tokiwa Y, Westerkamp T, Weickert F, Custers J, Ferstl J, Krellner C, Geibel C, Kerschl P, Müller K-H, Steglich F (2006) High-field phase diagram of the heavy-fermion metal \(\text{YbRh}_2\text{Si}_2\). New J Phys 8:171CrossRefGoogle Scholar
  70. 70.
    Shaginyan VR, Stephanovich VA, Popov KG, Kirichenko EV (2016) Quasi-one-dimensional quantum spin liquid in the \(\text{Cu}(\text{C}_4\text{H}_4\text{N}_2)(\text{NO}_3)_2\) insulator. JETP Lett 103:32–37CrossRefGoogle Scholar
  71. 71.
    Yamaguchi H, Okada M, Kono Y, Kittaka S, Sakakibara T, Okabe T, Iwasaki Y, Hosokoshi Y (2017) Randomness-induced quantum spin liquid on honeycomb lattice. Scientific reports 7. Article number: 16144Google Scholar
  72. 72.
    Uematsu K, Kawamura H (2017) Randomness-induced quantum spin liquid behavior in the \(s = 1/2\) random \(J_1-J_2\) Heisenberg antiferromagnet on the honeycomb lattice. J Phys Soc Jpn 86:044704CrossRefGoogle Scholar
  73. 73.
    Gomilsek M, Klanjsek M, Pregelj M, Luetkens H, Li Y, Zhang QM, Zorko A (2016) \(\mu \)SR insight into the impurity problem in quantum kagomé antiferromagnets. Phys Rev B 94:024438CrossRefGoogle Scholar
  74. 74.
    Han TH, Helton JS, Chu S, Nocera DG, Rodriguez-Rivera JA, Broholm C, Lee YS (2012) Fractionalized excitations in the spin-liquid state of a kagomé-lattice antiferromagnet. Nature 492:406–410CrossRefGoogle Scholar
  75. 75.
    Knafo W, Raymond S, Flouquet J, Fák B, Adams MA, Haen P, Lapierre F, Yates S, Lejay P (2004) Anomalous scaling behavior of the dynamical spin susceptibility of \(\text{Ce}_{0.925}\text{La}_{0.075}\text{Ru}_2\text{Si}_2\). Phys Rev B 70:174401CrossRefGoogle Scholar
  76. 76.
    Yamashita M, Nakata N, Senshu Y, Nagata M, Yamamoto HM, Kato R, Shibauchi T, Matsuda Y (2010) Highly mobile gapless excitations in a two-dimensional candidate quantum spin liquid. Science 328:1246–1248CrossRefGoogle Scholar
  77. 77.
    Yamashita M, Shibauchi T, Matsuda Y (2012) Probing non-equilibrium vibrational relaxation pathways in quantum spin liquids. Chem Phys 13:74–78Google Scholar
  78. 78.
    Imai T, Nytko EA, Bartlett BM, Shores MP, Nocera DG (2008) \(^{63}\text{Cu}\), \(^{35}\text{Cl}\), and \(^{\rm 1H}\) NMR in the \(S=1/2\) kagomé lattice \(\text{ZnCu}_3(\text{OH})_6\text{Cl}_2\). Phys Rev Lett 100:077203CrossRefGoogle Scholar
  79. 79.
    Carretta P, Pasero R, Giovannini M, Baines C (2009) Magnetic-field-induced crossover from non-Fermi to Fermi liquid at the quantum critical point of \(\text{YbCu}_{5-{x}}\text{Au}_{x}\). Phys Rev B 79:020401(R)CrossRefGoogle Scholar
  80. 80.
    Gegenwart P, Westerkamp T, Krellner C, Tokiwa Y, Paschen S, Geibel C, Steglich F, Abrahams E, Si Q (2007) Multiple energy scales at a quantum critical point. Science 315:969–971CrossRefGoogle Scholar
  81. 81.
    Shaginyan VR, Msezane AZ, Stephanovich VA, Popov KG, Japaridze GS (2018) Universal behavior of quantum spin liquid and optical conductivity in the insulator herbertsmithite. J Low Temp Phys 191:4–13CrossRefGoogle Scholar
  82. 82.
    Pilon DV, Lui CH, Han T-H, Shrekenhamer D, Frenzel AJ, Padilla WJ, Lee YS, Gedik N (2013) Spin-induced optical conductivity in the spin-liquid candidate Herbertsmithite. Phys Rev Lett 111:127401CrossRefGoogle Scholar
  83. 83.
    Ng T-K, Lee PA (2007) Power-law conductivity inside the Mott gap: application to \(\kappa{\hbox{-}}(\text{BEDT-TTF})_2\text{Cu}_2(\text{CN})_3\). Phys Rev Lett 99:156402CrossRefGoogle Scholar
  84. 84.
    Kézsmárki I, Shimizu Y, Mihály G, Tokura Y, Kanoda K, Saito G (2006) Depressed charge gap in the triangular-lattice Mott insulator \(\kappa{\hbox{-}}(\text{ET})_2\text{Cu}_2(\text{CN})_3\). Phys Rev B 74:201101(R)CrossRefGoogle Scholar
  85. 85.
    Oeschler N, Hartmann S, Pikul A, Krellner C, Geibel C, Steglich F (2008) Low-temperature specific heat of \(\text{YbRh}_2\text{Si}_2\). Phys B 403:1254–1256CrossRefGoogle Scholar
  86. 86.
    Yamashita M, Nakata N, Kasahara Y, Sasaki T, Yoneyama N, Kobayashi N, Fujimoto S, Shibauchi T, Matsuda Y (2009) Quantum criticality among entangled spin chains. Nat Phys 5:44–47CrossRefGoogle Scholar
  87. 87.
    Shimizu Y, Miyagawa K, Kanoda K, Maesato M, Saito G (2003) Spin liquid state in an organic Mott insulator with a triangular lattice. Phys Rev Lett 91:107001CrossRefGoogle Scholar
  88. 88.
    Yamashita S, Nakazawa Y, Oguni M, Oshima Y, Nojiri H, Shimizu Y, Miyagawa K, Kanoda K (2008) Thermodynamic properties of a spin-1/2 spin-liquid state in a \(\kappa \)-type organic salt. Nat Phys 4:459–462CrossRefGoogle Scholar
  89. 89.
    Smith MF, Paglione J, Walker MB, Taillefer L (2005) Origin of anomalous low-temperature downturns in the thermal conductivity of cuprates. Phys Rev B 71:014506CrossRefGoogle Scholar
  90. 90.
    Motrunich OI (2006) Orbital magnetic field effects in spin liquid with spinon Fermi sea: possible application to \(\kappa{\hbox{-}}({\rm ET})_2{\rm Cu}_2({\rm CN})_3\). Phys Rev B 73:155115CrossRefGoogle Scholar
  91. 91.
    Maegawa S, Itou T, Oyamada A, Kato R (2011) NMR study of quantum spin liquid and its phase transition in the organic spin-1/2 triangular lattice antiferromagnet \(\text{EtMe}_3\text{Sb}[\text{Pd(dmit)}_2]_2\). J Phys Conf Ser 320:012032CrossRefGoogle Scholar
  92. 92.
    Kubo R (1957) Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J Phys Soc Jpn 12:570–586CrossRefGoogle Scholar
  93. 93.
    Kono Y, Sakakibara T, Aoyama CP, Hotta C, Turnbull MM, Landee CP, Takano Y (2015) Field-induced quantum criticality and universal temperature dependence of the magnetization of a spin-1/2 Heisenberg Chain. Phys Rev Lett 114:037202CrossRefGoogle Scholar
  94. 94.
    Shechtman D, Blech I, Gratias D, Cahn JW (1984) Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett 53:1951–1953CrossRefGoogle Scholar
  95. 95.
    Shaginyan VR, Msezane AZ, Popov KG, Japaridze GS, Khodel VA (2013) Common quantum phase transition in quasicrystals and heavy-fermion metals. Phys Rev B 87:245122CrossRefGoogle Scholar
  96. 96.
    Krellner C, Lausberg S, Steppke A, Brando M, Pedrero L, Pfau H, Tencé S, Rosner H, Steglich F, Geibel C (2011) Ferromagnetic quantum criticality in the quasi-one-dimensional heavy fermion metal \(\text{YbNi}_4\text{P}_2\). New J Phys 13:103014CrossRefGoogle Scholar
  97. 97.
    Mennenga G, De Jongh L, Huiskamp W, Reedijk J (1984) Specific heat and susceptibility of the 1-dimensional S=1/2 Heisenberg antiferromagnet \(\text{Cu(Pyrazine)} (\text{NO}_3)_2\). Evidence for random exchange effects at low temperatures. J Magn Magn Mater 44:89–98CrossRefGoogle Scholar
  98. 98.
    Lancaster T, Blundell SJ, Brooks ML, Baker PJ, Pratt FL, Manson JL, Landee CP, Baines C (2006) Magnetic order in the quasi-one-dimensional spin-1/2 molecular chain compound copper pyrazine dinitrate. Phys Rev B 73:020410(R)CrossRefGoogle Scholar
  99. 99.
    Mattis DC, Lieb EH (1965) Exact solution of a many-fermion system and its associated boson field. J Math Phys 6:304–312CrossRefGoogle Scholar
  100. 100.
    Haldane FDM (1980) General relation of correlation exponents and spectral properties of one-dimensional fermi systems: application to the anisotropic \(S=1/2\) Heisenberg chain. Phys Rev Lett 45:1358–1362CrossRefGoogle Scholar
  101. 101.
    Haldane FDM (1981) Effective harmonic-fluid approach to low-energy properties of one-dimensional quantum fluids. Phys Rev Lett 47:1840–1843CrossRefGoogle Scholar
  102. 102.
    Affleck I (1991) Bose condensation in quasi-one-dimensional antiferromagnets in strong fields. Phys Rev B 43:3215–3222CrossRefGoogle Scholar
  103. 103.
    Giamarchi T (2003) Quantum physics in one dimension. Clarendon Press, OxfordCrossRefGoogle Scholar
  104. 104.
    Rozhkov AV (2005) Fermionic quasiparticle representation of Tomonaga–Luttinger Hamiltonian. Eur Phys J B 47:193–206CrossRefGoogle Scholar
  105. 105.
    Shaginyan VR, Msezane AZ, Popov KG, Stephanovich VA (2008) Universal behavior of two-dimensional \(^3\text{He}\) at low temperatures. Phys Rev Lett 100:096406CrossRefGoogle Scholar
  106. 106.
    Rozhkov AV (2014) One-dimensional fermions with neither Luttinger-liquid nor Fermi-liquid behavior. Phys Rev Lett 112:106403CrossRefGoogle Scholar
  107. 107.
    Lebed AG (2015) Non-Fermi-liquid crossovers in a quasi-one-dimensional conductor in a tilted magnetic field. Phys Rev Lett 115:157001CrossRefGoogle Scholar
  108. 108.
    Maeda Y, Hotta C, Oshikawa M (2007) Universal temperature dependence of the magnetization of gapped spin chains. Phys Rev Lett 99:057205CrossRefGoogle Scholar
  109. 109.
    Shaginyan VR, Msezane AZ, Popov KG, Clark JW, Khodel VA, Zverev MV (2016) Topological basis for understanding the behavior of the heavy-fermion metal \(\beta{\text{-}}\text{YbAlB}_4\) under application of magnetic field and pressure. Phys Rev B 93:205126CrossRefGoogle Scholar
  110. 110.
    Matsumoto Y, Nakatsuji S, Kuga K, Karaki Y, Horie N, Shimura Y, Sakakibara T, Nevidomskyy AH, Coleman P (2011) Quantum criticality without tuning in the mixed valence compound \(\beta{\text{-}}\text{YbAlB}_4\). Science 331:316–319CrossRefGoogle Scholar
  111. 111.
    Deguchi K, Matsukawa S, Sato NK, Hattori T, Ishida K, Takakura H, Ishimasa T (2012) Quantum critical state in a magnetic quasicrystal. Nat Mater 11:1013–1016CrossRefGoogle Scholar
  112. 112.
    Neumann M, Nyéki J, Cowan B, Saunders J (2007) Bilayer \(^3\text{He}\): a simple two-dimensional heavy-fermion system with quantum criticality. Science 317:1356–1359CrossRefGoogle Scholar
  113. 113.
    Takahashi D, Abe S, Mizuno H, Tayurskii D, Matsumoto K, Suzuki H, Onuki Y (2003) ac susceptibility and static magnetization measurements of \(\text{CeRu}_2\text{Si}_2\) at small magnetic fields and ultralow temperatures. Phys Rev B 67:180407(R)CrossRefGoogle Scholar
  114. 114.
    Ohtomo A, Hwang HY (2004) A high-mobility electron gas at the \(\text{LaAlO}_{3}/\text{SrTiO}_3\) heterointefrace. Nature (Lond) 427:423–426CrossRefGoogle Scholar
  115. 115.
    Luo Z-X, Lake E, Mei J-W, Starykh OA (2018) Spinon magnetic resonance of quantum spin liquids. Phys Rev Lett 120:037204CrossRefGoogle Scholar
  116. 116.
    Yu YJ, Xu Y, Ran KJ, Ni JM, Huang YY, Wang JH, Wen JS, Li SY (2018) Ultralow-temperature thermal conductivity of the Kitaev honeycomb magnet \(-\text{RuCl}_3\) across the field-induced phase transition. Phys Rev Lett 120:067202CrossRefGoogle Scholar
  117. 117.
    Hentrich R, Wolter AUB, Zotos X, Brenig W, Nowak D, Isaeva A, Doert T, Banerjee A, Lampen-Kelley P, Mandrus DG, Nagler SE, Sears J, Kim Y-J, Büchner B, Hess C (2018) Unusual phonon heat transport in \(\alpha{\text{-}}\text{RuCl}_3\): strong spin-phonon scattering and field-induced spin gap. Phys Rev Lett 120:117204CrossRefGoogle Scholar
  118. 118.
    Gu CC, Zhao ZY, Chen XL, Lee M, Choi ES, Han YY, Ling LS, Pi L, Zhang YH, Chen G, Yang ZR, Zhou HD, Sun XF (2018) Field-driven quantum criticality in the spinel magnet \(\text{ZnCr}_2\text{Se}_4\). Phys Rev Lett 120:147204CrossRefGoogle Scholar
  119. 119.
    Cao Y, Fatemi V, Demir A, Fang S, Tomarken SL, Luo JY, Sanchez-Yamagishi JD, Watanabe K, Taniguchi T, Kaxiras E, Ashoori RC, Jarillo-Herrero P (2018) Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556:80–84CrossRefGoogle Scholar
  120. 120.
    Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, Jarillo-Herrero P (2018) Unconventional superconductivity in magic-angle graphene superlattices. Nature 556:43–50CrossRefGoogle Scholar
  121. 121.
    Khalsa G, MacDonald AH (2012) Theory of the \(\text{SrTiO}_3\) surface state two-dimensional electron gas. Phys Rev B 86:125121CrossRefGoogle Scholar
  122. 122.
    Hwang HY, Iwasa Y, Kawasaki M, Keimer B, Nagaosa N, Tokura Y (2012) Emergent phenomena at oxide interfaces. Nat Mater 11:103–113CrossRefGoogle Scholar
  123. 123.
    Lu Li, Richter C, Mannhart J, Ashoori RC (2011) Coexistence of magnetic order and two-dimensional superconductivity at \(\text{LaAlO}_3/{\rm SrTiO}_3\) intefraces. Nat Phys 7:762–766CrossRefGoogle Scholar
  124. 124.
    Lee J-S, Xie YW, Sato HK, Bell C, Hikita Y, Hwang HY, Kao C-C (2013) Titanium \(d_{xy}\) ferromagnetism at the \(\text{LaAlO}_3/{\rm SrTiO}_3\) intefrace. Nat Mater 12:703–706CrossRefGoogle Scholar
  125. 125.
    Caviglia AD, Gariglio S, Reyren N, Jaccard D, Schneider T, Gabay M, Thiel S, Hammerl G, Mannhart J, Triscone J-M (2008) Electric field control of the \(\text{LaAlO}_3/{\rm SrTiO}_3\) interface ground state. Nature (Lond) 456:624–627CrossRefGoogle Scholar
  126. 126.
    Dikin DA, Mehta M, Bark CW, Folkman CM, Eom CB, Chandrasekhar V (2011) Coexistence of superconductivity and ferromagnetism in two dimensions. Phys Rev Lett 107:056802CrossRefGoogle Scholar
  127. 127.
    Stephanovich VA, Dugaev VK, Barnaś J (2016) Two-dimensional electron gas at the \(\text{LaAlO}_3/{\rm SrTiO}_3\) interface with a potential barrier. Phys Chem Chem Phys 18:2104–2111CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Petersburg Nuclear Physics Institute of NRC “Kurchatov Institute”GatchinaRussia
  2. 2.Clark Atlanta UniversityAtlantaUSA
  3. 3.Institute of PhysicsOpole UniversityOpolePoland
  4. 4.Department of Physics, McDonnell Center for the Space SciencesWashington UniversitySt. LouisUSA
  5. 5.Centro de Investigação em Matemática e AplicaçõesUniversity of MadeiraFunchalPortugal
  6. 6.Racah Institute of PhysicsHebrew UniversityJerusalemIsrael
  7. 7.Ioffe Physical Technical Institute, RASSt. PetersburgRussia

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