Fractionalization: spin liquids with deconfined spinons and non-collinear magnetic order in two-dimensional antiferromagnets

In addition to the confined states discussed earlier , an exciting possibility is that two-dimensional quantum paramagnets will have deconfined S=1/2 spinon excitations. These are charge neutral, S=1/2 excitations, and so the spin and charge of the underlying electrons have been fractionalized. The first definite model for such a phase was presented in paper 1, which related it to the deconfinement transition in a field theoretic model of a compact U(1) gauge theory coupled to a charge 2 Higgs field; as cited in paper 1, it was shown earlier in E. Fradkin and S. Shenker, Physical Review D 19, 3682 (1979) that the deconfinement transition in such a model is related to that in Z2 gauge theory, which is dual to the three-dimensional Ising model. In the present applications to quantum paramagnets, there are additional Berry phase terms that appear in the Z2 gauge theory (which appear in the form of frustrated couplings in the dual Ising model); this was shown in paper 3. Quite remarkably, the same "odd" Z2 gauge theory, with precisely the same Berry phase terms, appeared in the study of the interplay between antiferromagnetism and d-wave superconductivity in T. Senthil and Matthew P. A. Fisher Physical Review B 62, 7850 (2000).


  1. Large N expansion for frustrated quantum antiferromagnets, N. Read and S. Sachdev, Physical Review Letters 66, 1773 (1991).
  2. Large N expansion for frustrated and doped quantum antiferromagnets, S. Sachdev and N. Read, International Journal of Modern Physics B 5, 219 (1991); cond-mat/0402109.
  3. RVB and odd Z2 spin liquids, S. Sachdev, unpublished notes dated July 30, 1990. The final results of these notes were announced in paper 4, and full details were published in paper 10.
  4. Spontaneous alignment of frustrated bonds in an anisotropic, three dimensional Ising model, R. Jalabert and S. Sachdev, Physical Review B 44, 686 (1991).
  5. Kagome and triangular lattice Heisenberg antiferromagnets: ordering from quantum fluctuations and quantum-disordered ground states with deconfined bosonic spinons, S. Sachdev, Physical Review B 45, 12377 (1992).
  6. Quantum antiferromagnets in two dimensions, S. Sachdev, Low dimensional quantum field theories for condensed matter physicists, Yu Lu, S. Lundqvist, and G. Morandi eds., World Scientific, Singapore (1995); cond-mat/9303014.
  7. Universal magnetic properties of frustrated quantum antiferromagnets in two dimensions, A.V. Chubukov, T. Senthil and S. Sachdev, Physical Review Letters 72, 2089 (1994); cond-mat/9311045.
  8. Quantum phase transitions in frustrated, two-dimensional antiferromagnets, A.V. Chubukov, S. Sachdev, and T. Senthil, Nuclear Physics B 426, 601 (1994); cond-mat/9402006.
  9. Large S expansion for quantum antiferromagnets on a triangular lattice, A.V. Chubukov. S. Sachdev, and T. Senthil, Journal of Physics: Condensed Matter 6, 8891 (1994).
  10. Translational symmetry breaking in two-dimensional antiferromagnets and superconductors, S. Sachdev and M. Vojta, Journal of the Physical Society of Japan 69, Suppl. B, 1 (2000); cond-mat/9910231.
  11. Quantum criticality: competing ground states in low dimensions, S. Sachdev, Science 288, 475 (2000); cond-mat/0009456.
  12. Quantum phases of the Shastry-Sutherland antiferromagnet, C.H. Chung, J.B. Marston, and S. Sachdev, Physical Review B 64, 134407 (2001); cond-mat/0102222.
  13. Ground states of quantum antiferromagnets in two dimensions, S. Sachdev and K. Park, Annals of Physics (N.Y.) 298, 58 (2002); cond-mat/0108214.
  14. Bond and Neel order and fractionalization in easy-plane antiferromagnets in two dimensions, K. Park and S. Sachdev, Physical Review B 65, 220405 (2002); cond-mat/0112003.
  15. Fractionalized Fermi liquids, T. Senthil, S. Sachdev, and M. Vojta, Physical Review Letters 90, 216403 (2003); cond-mat/0209144.
  16. Absence of U(1) spin liquids in two dimensions, I. F. Herbut, B. H. Seradjeh, S. Sachdev, and G. Murthy, Physical Review B 68, 195110 (2003); cond-mat/0306537. This paper has been superseded by paper 168 (cond-mat/0312617) and M. Hermele et al., cond-mat/0404751.
  17. The planar pyrochlore antiferromagnet: A large-N analysis, J.-S. Bernier, C.-H. Chung, Y. B. Kim, and S. Sachdev, Physical Review B 69, 214427 (2004); cond-mat/0310504.
  18. Quantum phases and phase transitions of Mott insulators , S. Sachdev in Quantum magnetism, U. Schollwock, J. Richter, D. J. J. Farnell and R. A. Bishop eds, Lecture Notes in Physics, Springer, Berlin (2004), cond-mat/0401041.
  19. Low temperature broken symmetry phases of spiral antiferromagnets, L. Capriotti and S. Sachdev, Physical Review Letters 93, 257206 (2004); cond-mat/0409519.
  20. Dynamics and transport of the Z2 spin liquid: application to κ-(ET)2Cu2(CN)3, Y. Qi, C. Xu, and S. Sachdev, Physical Review Letters 102, 176401 (2009); arXiv:0809.0694.
  21. Global phase diagrams of frustrated quantum antiferromagnets in two dimensions: doubled Chern-Simons theory, C. Xu and S. Sachdev, Physical Review B 79, 064405 (2009); arXiv:0811.1220.
  22. Vison states and confinement transitions of Z2 spin liquids on the kagome lattice, Y. Huh, M. Punk and S. Sachdev, Physical Review B 84, 094419 (2011); arXiv:1106.3330.
  23. Optical conductivity of visons in Z2 spin liquids close to a VBS transition on the kagome lattice, Y. Huh, M. Punk, and S. Sachdev, Physical Review B 87, 235108 (2013); arXiv:1303.7235.
  24. Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice, M. Punk, D. Chowdhury, and S. Sachdev, Nature Physics 10, 289 (2014); arXiv:1308.2222.
  25. Probing excitations in insulators via injection of spin currents, S. Chatterjee and S. Sachdev, Physical Review B 92, 165113 (2015); arXiv:1506.04740.
  26. Emergent gauge fields and the high temperature superconductors, S. Sachdev, Philosophical Transactions of the Royal Society A 374, 20150248 (2016); arXiv:1512.00465.
  27. The novel metallic states of the cuprates: Fermi liquids with topological order and strange metals, S. Sachdev and D. Chowdhury, Progress of Theoretical and Experimental Physics 12C102 (2016); arXiv:1605.03579.