359 research outputs found
Reduced Density Matrices and Topological Order in a Quantum Dimer Model
Resonating valence bond (RVB) liquids in two dimensions are believed to
exhibit topological order and to admit no local order parameter of any kind.
This is a defining property of "liquids" but it has been explicitly confirmed
only in a few exactly solvable models. In this paper, we investigate the
quantum dimer model on the triangular lattice. It possesses an RVB-type liquid
phase, however, for which the absence of a local order parameter has not been
proved. We examine the question numerically with a measure based on reduced
density matrices. We find a scaling of the measure which strongly supports the
absence of any local order parameter.Comment: 6 pages, 3 figures. To appear in J. Phys.: Condens. Matter
(Proceedings of "Highly Frustrated Magnets", Osaka (Japan), August 2006).
Version 2: improved figures containing new data and minor changes in the tex
Low energy excitations of the kagome antiferromagnet and the spin gap issue
In this paper we report the latest results of exact diagonalizations of SU(2)
invariant models on various lattices (square, triangular, hexagonal,
checkerboard and kagome lattices). We focus on the low lying levels in each S
sector. The differences in behavior between gapless systems and gapped ones are
exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on
the kagome lattice is discussed. A rough estimate of the spin susceptibility in
such an hypothesis is given.The evolution of the intra-S channel spectra under
the effect of a small perturbation is consistent with the proximity of a
quantum critical point. We emphasize that the very small intra-S channel energy
scale observed in exact spectra is a very interesting information to understand
the low T dynamics of this model.Comment: 6 pages, 5 figures, revised version with a more extended discussion
on the issue of a possible proximity with a quantum critical point, a few
more details and references, a modified Fig
Exotic Mott phases of the extended t--J model on the checkerboard lattice at commensurate densities
Coulomb repulsion between electrons moving on a frustrated lattice can give
rise, at simple commensurate electronic densities, to exotic insulating phases
of matter. Such a phenomenon is illustrated using an extended t--J model on a
planar pyrochlore lattice for which the work on the quarter-filled case
[cond-mat/0702367] is complemented and extended to 1/8- and 3/8-fillings. The
location of the metal-insulator transition as a function of the Coulomb
repulsion is shown to depend strongly on the sign of the hopping. Quite
generally, the metal-insulator transition is characterized by lattice symmetry
breaking but the nature of the insulating Mott state is more complex than a
simple Charge Density Wave. Indeed, in the limit of large Coulomb repulsion,
the physics can be described in the framework of (extended) quantum
fully-packed loop or dimer models carrying extra spin degrees of freedom.
Various diagonal and off-diagonal plaquette correlation functions are computed
and the low-energy spectra are analyzed in details in order to characterize the
nature of the insulating phases. We provide evidence that, as for an electronic
density of n=1/2 (quarter-filling), the system at or exhibits
also plaquette order by forming a (lattice rotationally-invariant)
Resonating-Singlet-Pair Crystal, although with a quadrupling of the lattice
unit cell (instead of a doubling for ) and a 4-fold degenerate ground
state. Interestingly, qualitative differences with the bosonic analog (e.g.
known to exhibit columnar order at n=1/4) emphasize the important role of the
spin degrees of freedom in e.g. stabilizing plaquette phases w.r.t. rotational
symmetry-breaking phases.Comment: 7 pages, 7 figures Follow-up of cond-mat/070236
Monopole Flux State on the Pyrochlore Lattice
The ground state of a spin 1/2 nearest neighbor quantum Heisenberg
antiferromagnet on the pyrochlore lattice is investigated using a large
SU(N) fermionic mean field theory. We find several mean field states, of which
the state of lowest energy upon Gutzwiller projection, is a parity and time
reversal breaking chiral phase with a unit monopole flux exiting each
tetrahedron. This "monopole flux" state has a Fermi surface consisting of 4
lines intersecting at a point. At mean field the low-energy excitations about
the Fermi surface are gapless spinons. An analysis using the projective
symmetry group of this state suggests that the state is stable to small
fluctuations which neither induce a gap, nor alter the unusual Fermi surface
Hardcore dimer aspects of the SU(2) Singlet wavefunction
We demonstrate that any SU(2) singlet wavefunction can be characterized by a
set of Valence Bond occupation numbers, testing dimer presence/vacancy on pairs
of sites. This genuine quantum property of singlet states (i) shows that SU(2)
singlets share some of the intuitive features of hardcore quantum dimers, (ii)
gives rigorous basis for interesting albeit apparently ill-defined quantities
introduced recently in the context of Quantum Magnetism or Quantum Information
to measure respectively spin correlations and bipartite entanglement and, (iii)
suggests a scheme to define consistently a wide family of quantities analogous
to high order spin correlation. This result is demonstrated in the framework of
a general functional mapping between the Hilbert space generated by an
arbitrary number of spins and a set of algebraic functions found to be an
efficient analytical tool for the description of quantum spins or qubits
systems.Comment: 5 pages, 2 figure
Magnetization process from Chern-Simons theory and its application to SrCu2(BO3)2
In two-dimensional systems, it is possible transmute bosons into fermions by
use of a Chern-Simons gauge field. Such a mapping is used to compute
magnetization processes of two-dimensional magnets. The calculation of the
magnetization curve then involves the structure of the Hofstadter problem for
the lattice under consideration. Certain features of the Hofstadter butterfly
are shown to imply the appearance of magnetization plateaus. While not always
successfull, this approach leads to interesting results when applied to the 2D
AF magnet SrCu2(BO3)2.Comment: 10 pages, 7 figures, Proceedings of the 16th Nishinomiya-Yukawa
Memorial Symposium, Nishinomiya, Japan, Nov. 200
Sublattice Interference in the Kagome Hubbard Model
We study the electronic phases of the kagome Hubbard model (KHM) in the weak
coupling limit around van Hove filling. Through an analytic renormalization
group analysis, we find that there exists a sublattice interference mechanism
where the kagome sublattice structure affects the character of the Fermi
surface instabilities. It leads to major suppression of Tc for d+id
superconductivity in the KHM and causes an anomalous increase of Tc upon
addition of longer-range Hubbard interactions. We conjecture that the
suppression of conventional Fermi liquid instabilities makes the KHM a
prototype candidate for hosting exotic electronic states of matter at
intermediate coupling.Comment: 4+e pages, 3 figure
Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions
The extension of the Lieb-Schultz-Mattis theorem to dimensions larger than
one is discussed. It is explained why the variational wave-function built by
the previous authors is of no help to prove the theorem in dimension larger
than one. The short range R.V.B. picture of Sutherland, Rokhsar and Kivelson,
Read and Chakraborty gives a strong support to the assertion that the theorem
is indeed valid in any dimension. Some illustrations of the general ideas are
displayed on exact spectra.Comment: 12 pages, LaTeX with 4 EPS figures embedded in the documen
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