3,534 research outputs found
Bose-Hubbard model on two-dimensional line graphs
We construct a basis for the many-particle ground states of the positive
hopping Bose-Hubbard model on line graphs of finite 2-connected planar
bipartite graphs at sufficiently low filling factors. The particles in these
states are localized on non-intersecting vertex-disjoint cycles of the line
graph which correspond to non-intersecting edge-disjoint cycles of the original
graph. The construction works up to a critical filling factor at which the
cycles are close-packed.Comment: 9 pages, 5 figures, figures and conclusions update
Stability of Ferromagnetism in Hubbard models with degenerate single-particle ground states
A Hubbard model with a N_d-fold degenerate single-particle ground state has
ferromagnetic ground states if the number of electrons is less or equal to N_d.
It is shown rigorously that the local stability of ferromagnetism in such a
model implies global stability: The model has only ferromagnetic ground states,
if there are no single spin-flip ground states. If the number of electrons is
equal to N_d, it is well known that the ferromagnetic ground state is unique if
and only if the single-particle density matrix is irreducible. We present a
simplified proof for this result.Comment: accepted for publication in J. Phys.
Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands
We introduce and study two classes of Hubbard models with magnetic flux or
with spin-orbit coupling, which have a flat lowest band separated from other
bands by a nonzero gap. We study the Chern number of the flat bands, and find
that it is zero for the first class but can be nontrivial in the second. We
also prove that the introduction of on-site Coulomb repulsion leads to
ferromagnetism in both the classes.Comment: 6 pages, 5 figure
Quantum spin Hall effect and spin-charge separation in a kagome lattice
A two-dimensional kagome lattice is theoretically investigated within a
simple tight-binding model, which includes the nearest neighbor hopping term
and the intrinsic spin-orbit interaction between the next nearest neighbors. By
using the topological winding properties of the spin-edge states on the
complex-energy Riemann surface, the spin Hall conductance is obtained to be
quantized as () in insulating phases. This result keeps
consistent with the numerical linear-response calculation and the
\textbf{Z} topological invariance analysis. When the sample boundaries
are connected in twist, by which two defects with flux are introduced, we
obtain the spin-charge separated solitons at 1/3 (or 2/3) filling.Comment: 13 NJP pages, 7 figure
Gromov-Hausdorff convergence of discrete transportation metrics
This paper continues the investigation of `Wasserstein-like' transportation
distances for probability measures on discrete sets. We prove that the discrete
transportation metrics on the d-dimensional discrete torus with mesh size 1/N
converge, when , to the standard 2-Wasserstein distance W_2 on the
continuous torus in the sense of Gromov-Hausdorff. This is the first
convergence result for the recently developed discrete transportation metrics.
The result shows the compatibility between these metrics and the
well-established 2-Wasserstein metric.Comment: 22 pages, to appear in SIAM J. Math. Ana
Antiferromagnetism in the Exact Ground State of the Half Filled Hubbard Model on the Complete-Bipartite Graph
As a prototype model of antiferromagnetism, we propose a repulsive Hubbard
Hamiltonian defined on a graph \L={\cal A}\cup{\cal B} with and bonds connecting any element of with all the
elements of . Since all the hopping matrix elements associated with
each bond are equal, the model is invariant under an arbitrary permutation of
the -sites and/or of the -sites. This is the Hubbard model
defined on the so called -complete-bipartite graph,
() being the number of elements in (). In this
paper we analytically find the {\it exact} ground state for at
half filling for any ; the repulsion has a maximum at a critical
-dependent value of the on-site Hubbard . The wave function and the
energy of the unique, singlet ground state assume a particularly elegant form
for N \ra \inf. We also calculate the spin-spin correlation function and show
that the ground state exhibits an antiferromagnetic order for any non-zero
even in the thermodynamic limit. We are aware of no previous explicit analytic
example of an antiferromagnetic ground state in a Hubbard-like model of
itinerant electrons. The kinetic term induces non-trivial correlations among
the particles and an antiparallel spin configuration in the two sublattices
comes to be energetically favoured at zero Temperature. On the other hand, if
the thermodynamic limit is taken and then zero Temperature is approached, a
paramagnetic behavior results. The thermodynamic limit does not commute with
the zero-Temperature limit, and this fact can be made explicit by the analytic
solutions.Comment: 19 pages, 5 figures .ep
Flat-Bands on Partial Line Graphs -- Systematic Method for Generating Flat-Band Lattice Structures
We introduce a systematic method for constructing a class of lattice
structures that we call ``partial line graphs''.In tight-binding models on
partial line graphs, energy bands with flat energy dispersions emerge.This
method can be applied to two- and three-dimensional systems. We show examples
of partial line graphs of square and cubic lattices. The method is useful in
providing a guideline for synthesizing materials with flat energy bands, since
the tight-binding models on the partial line graphs provide us a large room for
modification, maintaining the flat energy dispersions.Comment: 9 pages, 4 figure
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