1,531 research outputs found
Laughlin's wave functions, Coulomb gases and expansions of the discriminant
In the context of the fractional quantum Hall effect, we investigate
Laughlin's celebrated ansatz for the groud state wave function at fractional
filling of the lowest Landau level. Interpreting its normalization in terms of
a one component plasma, we find the effect of an additional quadrupolar field
on the free energy, and derive estimates for the thermodynamically equivalent
spherical plasma. In a second part, we present various methods for expanding
the wave function in terms of Slater determinants, and obtain sum rules for the
coefficients. We also address the apparently simpler question of counting the
number of such Slater states using the theory of integral polytopes.Comment: 97 pages, using harvmac (with big option recommended) and epsf, 7
figures available upon request, Saclay preprint Spht 93/12
Yang-Baxter equation in spin chains with long range interactions
We consider the spin chains with long range interactions and the
spin generalization of the Calogero-Sutherland models. We show that their
properties derive from a transfer matrix obeying the Yang-Baxter equation. We
obtain the expression of the conserved quantities and we diagonalize them.Comment: Saclay-t93/00
Pairing states of a polarized Fermi gas trapped in a one-dimensional optical lattice
We study the properties of a one-dimensional (1D) gas of fermions trapped in
a lattice by means of the density matrix renormalization group method, focusing
on the case of unequal spin populations, and strong attractive interaction. In
the low density regime, the system phase-separates into a well defined
superconducting core and a fully polarized metallic cloud surrounding it. We
argue that the superconducting phase corresponds to a 1D analogue of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, with a quasi-condensate of
tightly bound bosonic pairs with a finite center-of-mass momentum that scales
linearly with the magnetization. In the large density limit, the system allows
for four phases: in the core, we either find a Fock state of localized pairs or
a metallic shell with free spin-down fermions moving in a fully filled
background of spin-up fermions. As the magnetization increases, the Fock state
disappears to give room for a metallic phase, with a partially polarized
superconducting FFLO shell and a fully polarized metallic cloud surrounding the
core.Comment: 4 pages, 5 fig
Correlation functions of the one-dimensional attractive Bose gas
The zero-temperature correlation functions of the one-dimensional attractive
Bose gas with delta-function interaction are calculated analytically for any
value of the interaction parameter and number of particles, directly from the
integrability of the model. We point out a number of interesting features,
including zero recoil energy for large number of particles, analogous to a
M\"ossbauer effect.Comment: 4 pages, 2 figure
Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle
We introduce an integrable lattice discretization of the quantum system of n
bosonic particles on a ring interacting pairwise via repulsive delta
potentials. The corresponding (finite-dimensional) spectral problem of the
integrable lattice model is solved by means of the Bethe Ansatz method. The
resulting eigenfunctions turn out to be given by specializations of the
Hall-Littlewood polynomials. In the continuum limit the solution of the
repulsive delta Bose gas due to Lieb and Liniger is recovered, including the
orthogonality of the Bethe wave functions first proved by Dorlas (extending
previous work of C.N. Yang and C.P. Yang).Comment: 25 pages, LaTe
Spin- and entanglement-dynamics in the central spin model with homogeneous couplings
We calculate exactly the time-dependent reduced density matrix for the
central spin in the central-spin model with homogeneous Heisenberg couplings.
Therefrom, the dynamics and the entanglement entropy of the central spin are
obtained. A rich variety of behaviors is found, depending on the initial state
of the bath spins. For an initially unpolarized unentangled bath, the
polarization of the central spin decays to zero in the thermodynamic limit,
while its entanglement entropy becomes maximal. On the other hand, if the
unpolarized environment is initially in an eigenstate of the total bath spin,
the central spin and the entanglement entropy exhibit persistent monochromatic
large-amplitude oscillations. This raises the question to what extent
entanglement of the bath spins prevents decoherence of the central spin.Comment: 8 pages, 2 figures, typos corrected, published versio
Emergence of Wigner molecules in one-dimensional systems of repulsive fermions under harmonic confinement
A Bethe-Ansatz spin-density functional approach is developed to evaluate the
ground-state density profile in a system of repulsively interacting spin-1/2
fermions inside a quasi-one-dimensional harmonic well. The approach allows for
the formation of antiferromagnetic quasi-order with increasing coupling
strength and reproduces with high accuracy the exact solution that is available
for the two-fermion system.Comment: 3 pages, 2 figures, submitte
Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions
A general procedure to get the explicit solution of the equations of motion
for N-body classical Hamiltonian systems equipped with coalgebra symmetry is
introduced by defining a set of appropriate collective variables which are
based on the iterations of the coproduct map on the generators of the algebra.
In this way several examples of N-body dynamical systems obtained from
q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2)
Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of
Ruijsenaars type arising from the same (non co-boundary) q-deformation of the
(1+1) Poincare' algebra. Also, a unified interpretation of all these systems as
different Poisson-Lie dynamics on the same three dimensional solvable Lie group
is given.Comment: 19 Latex pages, No figure
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