1,288 research outputs found
Magnetism of one-dimensional Wigner lattices and its impact on charge order
The magnetic phase diagram of the quarter-filled generalized Wigner lattice
with nearest- and next-nearest-neighbor hopping t_1 and t_2 is explored. We
find a region at negative t_2 with fully saturated ferromagnetic ground states
that we attribute to kinetic exchange. Such interaction disfavors
antiferromagnetism at t_2 <0 and stems from virtual excitations across the
charge gap of the Wigner lattice, which is much smaller than the Mott-Hubbard
gap proportional to U. Remarkably, we find a strong dependence of the charge
structure factor on magnetism even in the limit U to infinity, in contrast to
the expectation that charge ordering in the Wigner lattice regime should be
well described by spinless fermions. Our results, obtained using the
density-matrix renormalization group and exact diagonalization, can be
transparently explained by means of an effective low-energy Hamiltonian
Condensation of magnons and spinons in a frustrated ladder
Motivated by the ever-increasing experimental effort devoted to the
properties of frustrated quantum magnets in a magnetic field, we present a
careful and detailed theoretical analysis of a one-dimensional version of this
problem, a frustrated ladder with a magnetization plateau at m=1/2. We show
that even for purely isotropic Heisenberg interactions, the magnetization curve
exhibits a rather complex behavior that can be fully accounted for in terms of
simple elementary excitations. The introduction of anisotropic interactions
(e.g., Dzyaloshinskii-Moriya interactions) modifies significantly the picture
and reveals an essential difference between integer and fractional plateaux. In
particular, anisotropic interactions generically open a gap in the region
between the plateaux, but we show that this gap closes upon entering fractional
plateaux. All of these conclusions, based on analytical arguments, are
supported by extensive Density Matrix Renormalization Group calculations.Comment: 15 pages, 15 figures. minor changes in tex
Density matrix renormalisation group study of the correlation function of the bilinear-biquadratic spin-1 chain
Using the recently developed density matrix renormalization group approach,
we study the correlation function of the spin-1 chain with quadratic and
biquadratic interactions. This allows us to define and calculate the
periodicity of the ground state which differs markedly from that in the
classical analogue. Combining our results with other studies, we predict three
phases in the region where the quadratic and biquadratic terms are both
positive.Comment: 13 pages, Standard Latex File + 5 PostScript figures in separate (New
version with SUBSTANTIAL REVISIONS to appear in J Phys A
Enhanced Bound State Formation in Two Dimensions via Stripe-Like Hopping Anisotropies
We have investigated two-electron bound state formation in a square
two-dimensional t-J-U model with hopping anisotropies for zero electron
density; these anisotropies are introduced to mimic the hopping energies
similar to those expected in stripe-like arrangements of holes and spins found
in various transition metal oxides. In this report we provide analytical
solutions to this problem, and thus demonstrate that bound-state formation
occurs at a critical exchange coupling, J_c, that decreases to zero in the
limit of extreme hopping anisotropy t_y/t_x -> 0. This result should be
contrasted with J_c/t = 2 for either a one-dimensional chain, or a
two-dimensional plane with isotropic hopping. Most importantly, this behaviour
is found to be qualitatively similar to that of two electrons on the two-leg
ladder problem in the limit of t_interchain/t_intrachain -> 0. Using the latter
result as guidance, we have evaluated the pair correlation function, thus
determining that the bound state corresponds to one electron moving along one
chain, with the second electron moving along the opposite chain, similar to two
electrons confined to move along parallel, neighbouring, metallic stripes. We
emphasize that the above results are not restricted to the zero density limit -
we have completed an exact diagonalization study of two holes in a 12 X 2
two-leg ladder described by the t-J model and have found that the
above-mentioned lowering of the binding energy with hopping anisotropy persists
near half filling.Comment: 6 pages, 3 eps figure
Phases of two coupled Luttinger liquids
A model of two interacting one--dimensional fermion systems (``Luttinger
liquids'') coupled by single--particle hopping is investigated. Bosonization
allows a number of exact statements to be made. In particular, for forward
scattering only, the model contains two massless boson sectors and an Ising
type critical sector. For general interactions, there is a spin excitation gap
and either s-- or d--type pairing fluctuations dominate. It is shown that the
same behavior is also found for strong interactions. A possible scenario for
the crossover to a Fermi liquid in a many chain system is discussed.Comment: revised version, some changes, 11 pages, no figures, RexTeX3.
Charge-order transition in the extended Hubbard model on a two-leg ladder
We investigate the charge-order transition at zero temperature in a two-leg
Hubbard ladder with additional nearest-neighbor Coulomb repulsion V using the
Density Matrix Renormalization Group technique. We consider electron densities
between quarter and half filling. For quarter filling and U=8t, we find
evidence for a continuous phase transition between a homogeneous state at small
V and a broken-symmetry state with "checkerboard" [wavevector Q=(pi,pi)] charge
order at large V. This transition to a checkerboard charge-ordered state
remains present at all larger fillings, but becomes discontinuous at
sufficiently large filling. We discuss the influence of U/t on the transition
and estimate the position of the tricritical points.Comment: 4 pages, 5 figs, minor changes, accepted for publication in PRB R
Modularity clustering is force-directed layout
Two natural and widely used representations for the community structure of
networks are clusterings, which partition the vertex set into disjoint subsets,
and layouts, which assign the vertices to positions in a metric space. This
paper unifies prominent characterizations of layout quality and clustering
quality, by showing that energy models of pairwise attraction and repulsion
subsume Newman and Girvan's modularity measure. Layouts with optimal energy are
relaxations of, and are thus consistent with, clusterings with optimal
modularity, which is of practical relevance because both representations are
complementary and often used together.Comment: 9 pages, 7 figures, see http://code.google.com/p/linloglayout/ for
downloading the graph clustering and layout softwar
On the metal-insulator transition in the two-chain model of correlated fermions
The doping-induced metal-insulator transition in two-chain systems of
correlated fermions is studied using a solvable limit of the t-J model and the
fact that various strong- and weak-coupling limits of the two-chain model are
in the same phase, i.e. have the same low-energy properties. It is shown that
the Luttinger-liquid parameter K_\rho takes the universal value unity as the
insulating state (half-filling) is approached, implying dominant d-type
superconducting fluctuations, independently of the interaction strength. The
crossover to insulating behavior of correlations as the transition is
approached is discussed.Comment: 7 pages, 1 figur
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