689 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
Two-dimensional quantum antiferromagnets
This review presents some theoretical advances in the field of quantum
magnetism in two-dimensional systems, and quantum spin liquids in particular.
It is to be published as a chapter in the second edition of the book
"Frustrated spin systems", edited by H. T. Diep (World-Scientific). The section
(Sec. 7) devoted to the kagome antiferromagnet has been completely
rewritten/updated, as well as the concluding section (Sec. 8). The other
sections (Secs. 1-6) are unchanged from the first edition of the book
(published in 2005)Comment: 87 pages. 396 references. To be published as a chapter in the second
edition of the book "Frustrated spin systems", edited by H. T. Diep
(World-Scientific
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
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
Competing Valence Bond Crystals in the Kagome Quantum Dimer Model
The singlet dynamics which plays a major role in the physics of the spin-1/2
Quantum Heisenberg Antiferromagnet (QHAF) on the Kagome lattice can be
approximately described by projecting onto the nearest-neighbor valence bond
(NNVB) singlet subspace. We re-visit here the effective Quantum Dimer Model
which originates from the latter NNVB-projected Heisenberg model via a
non-perturbative Rokhsar-Kivelson-like scheme. By using Lanczos exact
diagonalisation on a 108-site cluster supplemented by a careful symmetry
analysis, it is shown that a previously-found 36-site Valence Bond Crystal
(VBC) in fact competes with a new type of 12-site "{\it resonating-columnar}"
VBC. The exceptionally large degeneracy of the GS multiplets (144 on our
108-site cluster) might reflect the proximity of the Z_2 dimer liquid.
Interestingly, these two VBC "emerge" in {\it different topological sectors}.
Implications for the interpretation of numerical results on the QHAF are
outlined.Comment: 8 pages, 5 figures, 4 tables; Figure 2 and Table II update
Multistability of Driven-Dissipative Quantum Spins
We study the dynamics of lattice models of quantum spins one-half, driven by
a coherent drive and subject to dissipation. Generically the meanfield limit of
these models manifests multistable parameter regions of coexisting steady
states with different magnetizations. We introduce an efficient scheme
accounting for the corrections to meanfield by correlations at leading order,
and benchmark this scheme using high-precision numerics based on
matrix-product-operators in one- and two-dimensional lattices. Correlations are
shown to wash the meanfield bistability in dimension one, leading to a unique
steady state. In dimension two and higher, we find that multistability is again
possible, provided the thermodynamic limit of an infinitely large lattice is
taken first with respect to the long time limit. Variation of the system
parameters results in jumps between the different steady states, each showing a
critical slowing down in the convergence of perturbations towards the steady
state. Experiments with trapped ions can realize the model and possibly answer
open questions in the nonequilibrium many-body dynamics of these quantum
systems, beyond the system sizes accessible to present numerics
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