292 research outputs found
Topological self-organization of strongly interacting particles
We investigate the self-organization of strongly interacting particles
confined in 1D and 2D. We consider hardcore bosons in spinless Hubbard lattice
models with short-range interactions. We show that many-body states with
topological features emerge at different energy bands separated by large gaps.
The topology manifests in the way the particles organize in real space to form
states with different energy. Each of these states contains topological
defects/condensations whose Euler characteristic can be used as a topological
number to categorize states belonging to the same energy band. We provide
analytical formulas for this topological number and the full energy spectrum of
the system for both sparsely and densely filled systems. Furthermore, we
analyze the connection with the Gauss-Bonnet theorem of differential geometry,
by using the curvature generated in real space by the particle structures. Our
result is a demonstration of how states with topological characteristics,
emerge in strongly interacting many-body systems following simple underlying
rules, without considering the spin, long-range microscopic interactions, or
external fields.Comment: 6 pages, 1 figure, some revisions, published in EPJ
Energetical self-organization of a few strongly interacting particles
We study the quantum self-organization of a few interacting particles with
strong short-range interactions. The physical system is modeled via a 2D
Hubbard square lattice model, with a nearest-neighbor interaction term of
strength U and a second nearest-neighbor hopping t. For t=0 the energy of the
system is determined by the number of bonds between particles that lie on
adjacent sites in the Hubbard lattice. We find that this bond order persists
for the ground and some of the excited states of the system, for strong
interaction strength, at different fillings of the system. For our analysis we
use the Euler characteristic of the network/graph grid structures formed by the
particles in real space (Fock states), which helps to quantify the
energetical(bond) ordering. We find multiple ground and excited states, with
integer Euler numbers, whose values persist from the case, for strong
interaction . The corresponding quantum phases for the ground state
contain either density-wave-order(DWO) for low fillings, where the particles
stay apart form each other, or clustering-order(CO) for high fillings, where
the particles form various structures as they condense into clusters. In
addition, we find various excited states containing superpositions of Fock
states, whose probability amplitudes are self-tuned in a way that preserves the
integer value of the Euler characteristic from the limit.Comment: 8 pages, 7 figures, some updates in the text and figures, published
in EPJ
Fractional-quantum-Hall-effect (FQHE) in 1D Hubbard models
We study the quantum self-organization of interacting particles in
one-dimensional(1D) many-body systems, modeled via Hubbard chains with
short-range interactions between the particles. We show the emergence of 1D
states with density-wave and clustering order, related to topology, at odd
denominator fillings that appear also in the fractional-quantum-Hall-effect
(FQHE), which is a 2D electronic system with Coulomb interactions between the
electrons and a perpendicular magnetic field. For our analysis we use an
effective topological measure applied on the real space wavefunction of the
system, the Euler characteristic describing the clustering of the interacting
particles. The source of the observed effect is the spatial constraints imposed
by the interaction between the particles. In overall, we demonstrate a simple
mechanism to reproduce many of the effects appearing in the FQHE, without
requiring a Coulomb interaction between the particles or the application of an
external magnetic field.Comment: 6 pages, 5 figures, small updates in the text and the references,
published in EPJ
Coherent wave transmission in quasi-one-dimensional systems with L\'evy disorder
We study the random fluctuations of the transmission in disordered
quasi-one-dimensional systems such as disordered waveguides and/or quantum
wires whose random configurations of disorder are characterized by density
distributions with a long tail known as L\'evy distributions. The presence of
L\'evy disorder leads to large fluctuations of the transmission and anomalous
localization, in relation to the standard exponential localization (Anderson
localization). We calculate the complete distribution of the transmission
fluctuations for different number of transmission channels in the presence and
absence of time-reversal symmetry. Significant differences in the transmission
statistics between disordered systems with Anderson and anomalous localizations
are revealed. The theoretical predictions are independently confirmed by tight
binding numerical simulations.Comment: 10 pages, 6 figure
Approximation Algorithms for Computing Maximin Share Allocations
We study the problem of computing maximin share allocations, a recently introduced fairness notion. Given a set of n agents and a set of goods, the maximin share of an agent is the best she can guarantee to herself, if she is allowed to partition the goods in any way she prefers, into n bundles, and then receive her least desirable bundle. The objective then is to find a partition, where each agent is guaranteed her maximin share. Such allocations do not always exist, hence we resort to approximation algorithms. Our main result is a 2/3-approximation that runs in polynomial time for any number of agents and goods. This improves upon the algorithm of Procaccia and Wang (2014), which is also a 2/3-approximation but runs in polynomial time only for a constant number of agents. To achieve this, we redesign certain parts of the algorithm in Procaccia and Wang (2014), exploiting the construction of carefully selected matchings in a bipartite graph representation of the problem. Furthermore, motivated by the apparent difficulty in establishing lower bounds, we undertake a probabilistic analysis. We prove that in randomly generated instances, maximin share allocations exist with high probability. This can be seen as a justification of previously reported experimental evidence. Finally, we provide further positive results for two special cases arising from previous works. The first is the intriguing case of three agents, where we provide an improved 7/8-approximation. The second case is when all item values belong to {0, 1, 2}, where we obtain an exact algorith
- …