Fractionalization: spin liquids with deconfined spinons and noncollinear magnetic order in
twodimensional antiferromagnets
In addition to the confined states discussed earlier
, an exciting possibility is that twodimensional 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 Z_{2} gauge theory,
which is dual to the threedimensional Ising model. In the present applications to quantum paramagnets, there are
additional Berry phase terms that appear in the Z_{2} 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" Z_{2} gauge theory, with precisely the same
Berry phase terms, appeared in the study of the interplay between antiferromagnetism and dwave
superconductivity in T. Senthil and Matthew P. A. Fisher Physical Review B 62, 7850 (2000).
PAPERS

Large N expansion for frustrated quantum antiferromagnets,
N. Read and S. Sachdev, Physical Review Letters 66, 1773 (1991).

Large N expansion for frustrated and doped quantum
antiferromagnets, S. Sachdev and N. Read, International Journal of
Modern Physics B 5, 219 (1991); condmat/0402109.

RVB and odd Z_{2} spin liquids, S. Sachdev, unpublished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.

Spontaneous alignment of frustrated bonds in an anisotropic,
three dimensional Ising model, R. Jalabert and S. Sachdev, Physical
Review B 44, 686 (1991).

Kagome and triangular lattice Heisenberg antiferromagnets:
ordering from quantum fluctuations and quantumdisordered ground states
with deconfined bosonic spinons, S. Sachdev, Physical Review B 45,
12377 (1992).

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); condmat/9303014.

Universal magnetic properties of frustrated quantum antiferromagnets
in two dimensions, A.V. Chubukov, T. Senthil and S. Sachdev, Physical
Review Letters 72, 2089 (1994); condmat/9311045.

Quantum phase transitions in frustrated, twodimensional
antiferromagnets, A.V. Chubukov, S. Sachdev, and T. Senthil, Nuclear
Physics B 426, 601 (1994); condmat/9402006.

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).

Translational symmetry breaking in twodimensional antiferromagnets
and superconductors, S. Sachdev and M. Vojta, Journal of the Physical
Society of Japan 69, Suppl. B, 1 (2000); condmat/9910231.

Quantum criticality: competing
ground states in low dimensions, S. Sachdev, Science 288, 475
(2000); condmat/0009456.

Quantum phases of the ShastrySutherland antiferromagnet, C.H. Chung, J.B. Marston, and S. Sachdev, Physical Review B 64, 134407 (2001); condmat/0102222.

Ground states of quantum antiferromagnets in
two dimensions, S. Sachdev and K. Park, Annals of Physics (N.Y.) 298, 58 (2002); condmat/0108214.

Bond and Neel order and fractionalization in easyplane antiferromagnets in two dimensions, K. Park and S. Sachdev, Physical Review B 65, 220405 (2002); condmat/0112003.

Fractionalized Fermi liquids, T. Senthil, S. Sachdev, and M. Vojta, Physical Review Letters 90, 216403 (2003); condmat/0209144.

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); condmat/0306537. This paper has been
superseded by paper 168 (condmat/0312617) and M. Hermele et al., condmat/0404751.
 The planar pyrochlore antiferromagnet: A largeN analysis, J.S. Bernier, C.H. Chung, Y. B. Kim, and S. Sachdev, Physical Review B 69, 214427 (2004); condmat/0310504.

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), condmat/0401041.

Low temperature broken symmetry phases of spiral antiferromagnets,
L. Capriotti and S. Sachdev, Physical Review Letters 93, 257206 (2004); condmat/0409519.
 Dynamics and transport of the Z_{2} spin liquid:
application to κ(ET)_{2}Cu_{2}(CN)_{3}, Y. Qi, C. Xu, and S. Sachdev,
Physical
Review Letters 102, 176401 (2009);
arXiv:0809.0694.
 Global phase diagrams of frustrated quantum antiferromagnets in two dimensions:
doubled ChernSimons theory, C. Xu and S. Sachdev, Physical Review B 79, 064405 (2009); arXiv:0811.1220.
 Vison states and confinement transitions of Z_{2} spin liquids on the kagome lattice,
Y. Huh, M. Punk and S. Sachdev, Physical Review B 84, 094419 (2011);
arXiv:1106.3330.
 Optical conductivity of visons in Z_{2} 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.
 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.
 Probing excitations in insulators via injection of spin currents,
S. Chatterjee and S. Sachdev, Physical Review B 92, 165113 (2015);
arXiv:1506.04740.
 Emergent gauge fields and the
high temperature superconductors, S. Sachdev, Philosophical Transactions of the Royal Society A 374,
20150248 (2016); arXiv:1512.00465.
 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.
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