Translational symmetry breaking and valencebondsolid (VBS) order in doped antiferromagnets
The theoretical strategy of these works is summarized in Figure 1.
Figure 1. Experimentally, the high temperature superconductors are produced
by doping the insulating compound La_{2}CuO_{4} with mobile holes. However, in this process, one crosses a quantum phase transition at which longrange magnetic order disappears. Theoretically it is more
convenient to first destroy the magnetic longrange order in the insulator by some other mechanism (e.g. by adding frustrating magnetic interactions), and to then dope with mobile carriers: this twostep theoretical process is sketched above. Details of the first step are discussed elsewhere in these web pages, while the second step is described in the papers below.
The first theoretical step in Figure 1 was discussed elsewhere in these web pages: it
was predicted in early work that destroying Neel
order in insulating, square lattice antiferromagnets leads to the appearance
of spinPeierls order (or more generally valencebondsolid (VBS) order). In addition, such paramagnetic insulators also necessarily possess a sharp S=1 collective spin resonance, and the confinement of a S=1/2 moment near each nonmagnetic impurity (discussed elsewhere). The papers below discuss the consequences
of doping such a VBS state by mobile holes: VBS order, confinement of S=1/2 moments near nonmagnetic impurities, and the sharp S=1 resonance survive for a finite range of doping, and coexist with dwavelike superconductivity.
A first analysis of the doping of the nonmagnetic VBSordered Mott insulator
appeared in paper 2, and the results are summarized in Figure 2 below.
Figure 2. Phase diagram from paper 2 of the doping of a VBSordered
Mott insulator, as described by the tJ model. It is instructive to follow the phases as
a function of the doping d for large values of t/J. Initially, there
is a superconducting state which coexists with VBS ordering.
Here the superconducting order
is dwave like (that is, the pairing amplitudes in the x
and y directions have opposite signs) and it coexists with VBS order:
such a state was first discussed
in paper 2. With increasing
doping, the amplitude of the VBS order decreases and gapless fermionic
excitations appear at nodal points, which are first generated at the edges
of the Brillouin zone. Eventually there is a phase transition to an isotropic
dwave superconductor.
The computation also found an instability to phase
separation below the dotted line.
A more complete analysis of the phase diagram requires a more careful consideration
of the influence of the longrange
Coulomb interactions, and of the possibility of VBSordered states with
larger periods. Such an analysis was carried out
in papers 3,4, and the results are summarized in Figure 3 below.
Figure 3. Phase diagram analogous to Figure 1 above from papers 3,4. The vertical axis represents
an arbitrary shortrange exchange interaction which can destroy the longrange Neel order in
the insulator. A specific example is the study of A. W. Sandvik, S. Daul, R. R. P. Singh, and D. J. Scalapino, Physical Review Letters 89, 247201 (2002), which used a ring exchange interaction: as expected from the arguments in this web page, the large ring exchange phase had
VBS order, as shown in the figure above.
The computations of papers 3,4 were carried out in the unhatched region (which has no long range
magnetic order) and sample configurations of the VBS order are shown; the states shown pick one
directions as special, but "checkerboard" states also appear (M. Vojta, Physical Review B 66, 104505 (2002)). The physics of the transition from the hatched to the unhatched regions (involving restoration of spin rotation
invariance) is discussed in the web pages on collinear magnetic order, noncollinear magnetic order, quantum criticality, and the influence of an applied magnetic field . While the meanfield studies of VBS order
lead to a bondcentered modulation of the lattice spacings (shown above), there can be "resonance"
between different meanfield configurations, and the symmetry of bond modulations can
also be such that the reflection symmetry is about a site.
Notice the more elaborate types of VBS order in the nonmagnetic superconductor. It is expected that
the primary modulation in these VBSordered states will be in the exchange, kinetic, and pairing energies
between sites, rather than the onsite charge densities. This issue should be distinguished from the issue
of the lattice symmetry of the modulation, which could have a plane of reflection symmetry about
either the bonds or the sites.
While the VBS states discussed above break the symmetry between the x and y
lattice directions, they are not necessarily ``quasi onedimensional'' i.e. the basic instability leading to VBS ordering in the undoped
paramagnet is genuinely twodimensional. Furthermore, "checkerboard" states can also appear
(M. Vojta, Physical Review B 66, 104505 (2002)).
See also the article by Barbara Levi in Physics Today, volume 57, number 9, page 24 (2004).
PAPERS

Large N limit of the square lattice tJ
model at 1/4 and other filling fractions, S. Sachdev, Phys. Rev. B
41,
4502 (1990).

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.

Charge order, superconductivity, and a global phase diagram
of doped antiferromagnets, M. Vojta and S. Sachdev, Physical Review
Letters 83, 3916 (1999); condmat/9906104.

Competing orders and quantum criticality in doped antiferromagnets,
M. Vojta, Y. Zhang, and S. Sachdev, Physical Review B 62, 6721 (2000);
condmat/0003163.

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
phase transitions, S. Sachdev, Physics World 12, No 4, 33 (April
1999).

Quantum phase transitions in
antiferromagnets and superfluids, S. Sachdev and M. Vojta, Physica
B 280, 333 (2000); condmat/9908008.

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

Bond operator theory of doped antiferromagnets: from Mott insulators with bondcentered charge order, to superconductors with nodal fermions, K. Park and S. Sachdev, Physical Review B 64, 184510 (2001); condmat/0104519.

Spin and charge order in Mott insulators and dwave
superconductors, S. Sachdev, Proceedings of Spectroscopies of Novel Superconductors, Chicago, May 1317, 2001, Journal of Physics and Chemistry of Solids 63, 2269 (2002); condmat/0108238.

Pinning of dynamic spin density wave fluctuations in the cuprate superconductors, A. Polkovnikov, M. Vojta, and S. Sachdev, Physical Review B 65, 220509 (2002);
condmat/0203176.

Strongly coupled quantum criticality with a Fermi surface in two
dimensions: fractionalization of spin and charge collective modes, S. Sachdev and T. Morinari, Physical Review B 66, 235117 (2002);
condmat/0207167.

Spin collective mode and quasiparticle contributions to STM spectra of
dwave superconductors with pinning, A. Polkovnikov, S. Sachdev, and M. Vojta, Proceedings
of the 23rd International Conference
on Low Temperature Physics, August 2027, 2002,
Hiroshima, Japan, Physica C 388389, 19 (2003) (Erratum: 391, 381 (2003)); condmat/0208334.

Order and quantum phase transitions in the cuprate superconductors, S. Sachdev, Reviews of Modern Physics 75, 913 (2003); condmat/0211005.

Order and quantum phase transitions in the cuprate superconductors (summary), S. Sachdev, Solid State Communications 127, 169 (2003), Proceedings of the Euroconference on Quantum
Phases at the Nanoscale,
Erice, Italy, 1520 July 2002.

Understanding correlated electron systems by a classification of Mott insulators, S. Sachdev, Annals of Physics 303, 226 (2003); condmat/0211027.

Field theories of paramagnetic Mott insulators, S. Sachdev, Proceedings of the
International Conference on Theoretical Physics, Paris, UNESCO, 2227 July 2002, Annales Henri
Poincare 4, 559 (2003); condmat/0304137.

Putting competing orders in their place near the Mott transition, L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Physical Review B 71, 144508 (2005); condmat/0408329.

Phenomenological lattice model for dynamic spin and charge fluctuations in the cuprates, M. Vojta and S. Sachdev, Proceedings of Spectroscopies of Novel Superconductors, Sitges, Spain, July 1116, 2004, Journal of the Physics and Chemistry of Solids, 67, 11 (2006); condmat/0408461.

Putting competing orders in their place near the Mott transition II: The doped quantum dimer model, L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Physical Review B 71, 144509 (2005); condmat/0409470.

Thermal melting of density waves on the square lattice,
A. Del Maestro and S. Sachdev, Physical Review B 71, 184511 (2005); condmat/0412498.

Estimating the mass of vortices in the cuprate superconductors, L. Bartosch, L. Balents, and
S. Sachdev, condmat/0502002.

Competing Orders and nonLandauGinzburgWilson Criticality in (Bose) Mott transitions ,
L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta,
Proceedings of ``Physics of Strongly Correlated Electron Systems'', YKIS2004 workshop,
Yukawa Institute, Kyoto, Japan, November 2004, Progress of Theoretical Physics Supplement 160,
314 (2005); condmat/0504692.

Detecting the quantum zeropoint motion of vortices in the cuprate superconductors, L. Bartosch, L. Balents, and
S. Sachdev, Annals of Physics 321, 1528 (2006); condmat/0602429.

From stripe to checkerboard order on the square lattice, in the presence of
quenched disorder, A. Del Maestro, B. Rosenow, and S. Sachdev, Physical Review B 74, 024520 (2006);
condmat/0603029.
 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.
 Bond order in twodimensional metals with antiferromagnetic exchange interactions,
S. Sachdev and R. La Placa, Physical Review Letters 111, 027202 (2013);
arXiv:1303.2114.
 Angular fluctuations of a multicomponent order describe the pseudogap regime of the cuprate superconductors,
L. E. Hayward, D. G. Hawthorn, R. G. Melko, and S. Sachdev, Science 343 , 1336 (2014); arXiv:1309.6639.
 Mean field theory of competing orders in metals with antiferromagnetic
exchange interactions,
J. D. Sau and S. Sachdev, Physical Review B 89, 075129 (2014);
arXiv:1311.3298.
 Quantum quenches and competing orders,
LingYan Hung, Wenbo Fu, and S. Sachdev, Physical Review B 90, 024506 (2014); arXiv:1402.0875.
 Bond order instabilities in a correlated twodimensional metal,
A. Allais, J. Bauer, and S. Sachdev, Physical Review B 90, 155114 (2014); arXiv:1402.4807.
 Auxiliaryboson and DMFT studies of bond ordering instabilities of tJV models on the square lattice,
A. Allais, J. Bauer, and S. Sachdev,
Indian Journal of Physics 88, 905 (2014);
arXiv:1402.6311.
 Fermi Surface and Pseudogap Evolution in a Cuprate Superconductor,
Yang He, Yi Yin, M. Zech, A. Soumyanarayanan, I. Zeljkovic, M. M. Yee, M. C. Boyer, K. Chatterjee, W. D. Wise, Takeshi Kondo, T. Takeuchi,
H. Ikuta, P. Mistark, R. S. Markiewicz, A. Bansil, S. Sachdev, E. W. Hudson, and J. E. Hoffman, Science
344, 608 (2014);
arXiv:1305.2778.
 Direct phase sensitive identification of a dform factor density wave in underdoped cuprates,
K. Fujita, M. H. Hamidian, S. D. Edkins, Chung Koo Kim, Y. Kohsaka, M. Azuma, M. Takano, H. Takagi, H. Eisaki, S. Uchida,
A. Allais, M. J. Lawler, E.A. Kim, S. Sachdev, and J. C. Seamus Davis,
Proceedings of the National Academy of Sciences 111, E3026 (2014);
arXiv:1404.0362.
 Feedback of superconducting fluctuations on charge order in the underdoped cuprates,
D. Chowdhury and S. Sachdev, Physical Review B 90, 134516 (2014); arXiv:1404.6532.
 Connecting highfield quantum oscillations to the pseudogap in the underdoped cuprates,
A. Allais, D. Chowdhury, and S. Sachdev, Nature Communications 5, 5771 (2014); arXiv:1406.0503.
 Diamagnetism and density wave order in the pseudogap regime of YBa_{2}Cu_{3}O_{6+x},
L. E. Hayward, A. J. Achkar, D. G. Hawthorn, R. G. Melko, and S. Sachdev, Physical Review B 90, 094515 (2014);
arXiv:1406.2694.
 Renormalization Group Analysis of a Fermionic Hot Spot Model,
S. Whitsitt and S. Sachdev,
Physical Review B 90, 104505 (2014);
arXiv:1406.6061.
 Comment on "Symmetry classification of bond order parameters in
cuprates",
A. Allais, J. Bauer, and S. Sachdev, arXiv:1407.3281.
 Density wave instabilities of fractionalized Fermi liquids,
D. Chowdhury and S. Sachdev, Physical Review B 90, 245136 (2014); arXiv:1409.5430.
 Charge ordering in threeband models of the cuprates,
A. Thomson and S. Sachdev, Physical Review B 91, 115142 (2015); arXiv:1410.3483.
 The enigma of the pseudogap phase of the cuprate superconductors,
D. Chowdhury and S. Sachdev, in Quantum Criticality in Condensed Matter: Phenomena, Materials and Ideas in Theory and Experiment: 50th Karpacz Winter School of Theoretical Physics, J. Jedrzejewski Editor, World Scientific (2015),
arXiv:1501.00002
 Fluctuating orders and quenched randomness in the cuprates,
Laimei Nie, L. E. H. Sierens, R. G. Melko, S. Sachdev, and S. A. Kivelson, Physical Review B 92, 174505 (2015);
arXiv:1505.06206.
 Real space Eliashberg approach to charge order of electrons coupled to dynamic antiferromagnetic fluctuations,
J. Bauer and S. Sachdev, Physical Review B 92, 085134 (2015); arXiv:1506.06136.
 Atomicscale Electronic Structure of the Cuprate dSymmetry Form Factor Density Wave State,
M. H. Hamidian, S. D. Edkins, Chung Koo Kim, J. C. Davis, A. P. Mackenzie,
H. Eisaki, S. Uchida, M. J. Lawler, E.A. Kim, S. Sachdev, and K. Fujita, Nature Physics 12, 150 (2016); arXiv:1507.07865
 Magneticfield Induced Interconversion of Cooper Pairs and Density Wave States within Cuprate Composite Order,
M. H. Hamidian, S. D. Edkins, K. Fujita, A. Kostin, A. P. Mackenzie,
H. Eisaki, S. Uchida, M. J. Lawler, E.A. Kim, S. Sachdev, and J. C. Davis, arXiv:1508.00620
 Emergent gauge fields and the
high temperature superconductors, S. Sachdev, Philosophical Transactions of the Royal Society A 374,
20150248 (2016); arXiv:1512.00465.
 Confinement transition to density wave order in metallic doped spin liquids, Physical Review B 93,
165139 (2016); A. A. Patel, D. Chowdhury, A. Allais, and S. Sachdev, arXiv:1602.05954.
NEXT ; PREVIOUS ; CATEGORIES