33,688 research outputs found
Number-parity effect for confined fermions in one dimension
For spin-polarized fermions with harmonic pair interactions in a
-dimensional trap an odd-even effect is found. The spectrum of the
-particle reduced density matrix of the system's ground state differs
qualitatively for odd and even. This effect does only occur for strong
attractive and repulsive interactions. Since it does not exists for bosons, it
must originate from the repulsive nature implied by the fermionic exchange
statistics. In contrast to the spectrum, the -particle density and
correlation function for strong attractive interactions do not show any
sensitivity on the number parity. This also suggests that
reduced-density-matrix-functional theory has a more subtle -dependency than
density functional theory.Comment: published versio
Duality of reduced density matrices and their eigenvalues
For states of quantum systems of particles with harmonic interactions we
prove that each reduced density matrix obeys a duality condition. This
condition implies duality relations for the eigenvalues of
and relates a harmonic model with length scales with
another one with inverse lengths . Entanglement
entropies and correlation functions inherit duality from . Self-duality
can only occur for noninteracting particles in an isotropic harmonic trap
New fermionic formula for unrestricted Kostka polynomials
A new fermionic formula for the unrestricted Kostka polynomials of type
is presented. This formula is different from the one given by
Hatayama et al. and is valid for all crystal paths based on
Kirillov-Reshetihkin modules, not just for the symmetric and anti-symmetric
case. The fermionic formula can be interpreted in terms of a new set of
unrestricted rigged configurations. For the proof a statistics preserving
bijection from this new set of unrestricted rigged configurations to the set of
unrestricted crystal paths is given which generalizes a bijection of Kirillov
and Reshetikhin.Comment: 35 pages; reference adde
A bijection between type D_n^{(1)} crystals and rigged configurations
Hatayama et al. conjectured fermionic formulas associated with tensor
products of U'_q(g)-crystals B^{r,s}. The crystals B^{r,s} correspond to the
Kirillov--Reshetikhin modules which are certain finite dimensional
U'_q(g)-modules. In this paper we present a combinatorial description of the
affine crystals B^{r,1} of type D_n^{(1)}. A statistic preserving bijection
between crystal paths for these crystals and rigged configurations is given,
thereby proving the fermionic formula in this case. This bijection reflects two
different methods to solve lattice models in statistical mechanics: the
corner-transfer-matrix method and the Bethe Ansatz.Comment: 38 pages; version to appear in J. Algebr
Crystal structure on rigged configurations
Rigged configurations are combinatorial objects originating from the Bethe
Ansatz, that label highest weight crystal elements. In this paper a new
unrestricted set of rigged configurations is introduced for types ADE by
constructing a crystal structure on the set of rigged configurations. In type A
an explicit characterization of unrestricted rigged configurations is provided
which leads to a new fermionic formula for unrestricted Kostka polynomials or
q-supernomial coefficients. The affine crystal structure for type A is obtained
as well.Comment: 20 pages, 1 figure, axodraw and youngtab style file necessar
Hubbard model: Pinning of occupation numbers and role of symmetries
Fermionic natural occupation numbers do not only obey Pauli's exclusion
principle, but are even further restricted by so-called generalized Pauli
constraints. Such restrictions are particularly relevant whenever they are
saturated by given natural occupation numbers . For
few-site Hubbard models we explore the occurrence of this pinning effect. By
varying the on-site interaction for the fermions we find sharp transitions
from pinning of to the boundary of the allowed region to
nonpinning. We analyze the origin of this phenomenon which turns out be either
a crossing of natural occupation numbers or
a crossing of -particle energies. Furthermore, we emphasize the relevance of
symmetries for the occurrence of pinning. Based on recent progress in the field
of ultracold atoms our findings suggest an experimental set-up for the
realization of the pinning effect.Comment: published versio
q-Supernomial coefficients: From riggings to ribbons
q-Supernomial coefficients are generalizations of the q-binomial
coefficients. They can be defined as the coefficients of the Hall-Littlewood
symmetric function in a product of the complete symmetric functions or the
elementary symmetric functions. Hatayama et al. give explicit expressions for
these q-supernomial coefficients. A combinatorial expression as the generating
function of ribbon tableaux with (co)spin statistic follows from the work of
Lascoux, Leclerc and Thibon. In this paper we interpret the formulas by
Hatayama et al. in terms of rigged configurations and provide an explicit
statistic preserving bijection between rigged configurations and ribbon
tableaux thereby establishing a new direct link between these combinatorial
objects.Comment: 19 pages, svcon2e.sty file require
Rigged configurations and the Bethe Ansatz
These notes arose from three lectures presented at the Summer School on
Theoretical Physics "Symmetry and Structural Properties of Condensed Matter"
held in Myczkowce, Poland, on September 11-18, 2002. We review rigged
configurations and the Bethe Ansatz. In the first part, we focus on the
algebraic Bethe Ansatz for the spin 1/2 XXX model and explain how rigged
configurations label the solutions of the Bethe equations. This yields the
bijection between rigged configurations and crystal paths/Young tableaux of
Kerov, Kirillov and Reshetikhin. In the second part, we discuss a
generalization of this bijection for the symmetry algebra , based on
work in collaboration with Okado and Shimozono.Comment: 24 pages; lecture notes; axodraw style file require
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