Confining paramagnets and Neel and valence-bond-solid (VBS) order in two-dimensional
The S=1/2 antiferromagnet on the square lattice is known to have
a ground state with Neel long-range order, in which the average spin moments
are collinearly polarized in a staggered checkerboard pattern. Suppose
we now add frustrating second or further neighbor interactions which destroy
the magnetic order in a continuous quantum phase transition, and produce
a spin singlet ground state in which average moment on each site is zero.
What is the nature of such a ground state ? The following papers argue
that, on rather general grounds, destroying collinearly polarized
magnetic order leads to a paramagnetic ground state with the following
A great deal of numerical work has been done on the above questions, and
two recent references are M.S.L. du Croo de Jongh et al, Physical Review B 62, 14844 (2000),
and O.P. Sushkov et al, Physical Review B 63, 104420 (2001).
Broken translational symmetry due to the appearance of valence-bond-solid (VBS) order
with at least a four-fold degenerate ground
state. A simple possibility is that the ground state is a columnar spin-Peierls
state: this state is preferred because
it maximizes the "resonance" between nearest neighbor singlet pairings
around a plaquette.
Excited states with non-zero spin are created by breaking a singlet bond
between a pair of spins. The two S=1/2 moments at the ends of this
broken bond ("spinons") are unable to move away from each other (the spinons
are confined), and so the lowest excitation is a stable S=1 particle.
This particle will appear as a sharp resonance in the neutron scattering
cross-section, above a finite energy gap at the magnetic ordering wavevector.
have argued that this resonance is related to observations on the high
An experimental study of a pressure-tuned phase diagram of insulating (TMTTF)2PF6
by D.S. Chow et al, Physical Review Letters 81, 3984 (1999), yielded results very similar to the theoretical phase diagram above with Neel and spin-Peierls order.
for VBS order in doped antiferromagnets is discussed in a separate
NEXT ; PREVIOUS ; CATEGORIES
Some features of the phase diagram of SU(N) antiferromagnets
on a square lattice, N. Read and S. Sachdev, Nuclear Physics B 316,
Hole motion in a quantum Neel state, S. Sachdev,
Physical Review B 39, 12232 (1989).
Valence bond and spin-Peierls ground states of low dimensional
quantum antiferromagnets, N. Read and S. Sachdev, Physical Review Letters
Sine-Gordon theory of the non-Neel phase of two-dimensional
quantum antiferromagnets, W. Zheng and S. Sachdev, Physical Review
B 40, 2704 (1989).
Spin-Peierls ground states of the quantum dimer model:
a finite size study, S. Sachdev, Physical Review B 40, 5204
Bond-operator representation of quantum spins: Mean field
theory of frustrated quantum Heisenberg antiferromagnets, S. Sachdev
and R.N. Bhatt, Physical Review B 41, 9323 (1990).
Action of hedgehog-instantons in the disordered phase
of the 2+1 dimensional CPN-1 model, G. Murthy and
S. Sachdev, Nuclear Physics B 344, 557 (1990).
Spin-Peierls, valence bond solid, and Neel ground states
of low dimensional quantum antiferromagnets, N. Read and S. Sachdev,
Physical Review B 42, 4568 (1990).
Effective lattice models for two dimensional quantum
antiferromagnets, S. Sachdev and R. Jalabert, Modern Physics Letters
B 4, 1043 (1990).
Nature of the disordered phase
of low dimensional quantum antiferromagnets, S. Sachdev, Electron
Correlation and Disorder Effects in Metals, S.N. Behera ed., World
Scientific, Singapore (1990).
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.
Finite temperature properties of quantum antiferromagnets
in a uniform magnetic field in one and two dimensions, S. Sachdev,
T. Senthil, and R. Shankar, Physical Review B 50, 258 (1994); cond-mat/9401040.
Spin-Peierls states of quantum antiferromagnets on the
CaV4O9 lattice, S. Sachdev and N. Read, Physical
Review Letters 77, 4800 (1996); cond-mat/9604134.
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.
Quantum criticality: competing
ground states in low dimensions, S. Sachdev, Science 288, 475
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.
Ground states of quantum antiferromagnets in
two dimensions, S. Sachdev and K. Park, Annals of Physics (N.Y.) 298, 58 (2002); cond-mat/0108214.
Quantum phase transitions of correlated electrons in two dimensions, S. Sachdev, Lectures at the International Summer School on Fundamental Problems
in Statistical Physics X, August-September 2001, Altenberg, Germany, Physica A 313, 252 (2002); cond-mat/0109419.
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.
Order and quantum phase transitions in the cuprate superconductors, S. Sachdev, Reviews of Modern Physics 75, 913 (2003); cond-mat/0211005.
Field theories of paramagnetic Mott insulators, S. Sachdev, Proceedings of the
International Conference on Theoretical Physics, Paris, UNESCO, 22-27 July 2002, Annales Henri
Poincare 4, 559 (2003); cond-mat/0304137.
`Deconfined' quantum critical points , T. Senthil, A. Vishwanath, L. Balents, S. Sachdev,
and M. P. A. Fisher, Science 303, 1490 (2004); cond-mat/0311326.
- 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.
Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm, T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Physical Review B 70, 144407 (2004); cond-mat/0312617.
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.
Deconfined criticality critically defined, T. Senthil, L. Balents, S. Sachdev, A. Vishwanath, and M. P. A. Fisher, Journal of the Physics Society of Japan 74
Suppl. 1 (2005); cond-mat/0404718.
- Theory of Neel and valence-bond-solid phases on the kagome lattice of Zn-paratacamite,
M. J. Lawler, L. Fritz, Y. B. Kim, and S. Sachdev, Physical Review Letters 100, 187201 (2008); arXiv:0709.4489.