5,551 research outputs found
Jack polynomials with prescribed symmetry and hole propagator of spin Calogero-Sutherland model
We study the hole propagator of the Calogero-Sutherland model with SU(2)
internal symmetry. We obtain the exact expression for arbitrary non-negative
integer coupling parameter and prove the conjecture proposed by one of
the authors. Our method is based on the theory of the Jack polynomials with a
prescribed symmetry.Comment: 12 pages, REVTEX, 1 eps figur
Some Properties of the Calogero-Sutherland Model with Reflections
We prove that the Calogero-Sutherland Model with reflections (the BC_N model)
possesses a property of duality relating the eigenfunctions of two Hamiltonians
with different coupling constants. We obtain a generating function for their
polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of
the wave-functions for certain particular cases (associated to the root systems
of the classical Lie groups B_N, C_N and D_N) is also discussed.Comment: 16 pages, harvmac.te
Scattering of hole excitations in a one-dimensional spinless quantum liquid
Luttinger liquid theory accounts for the low energy boson excitations of
one-dimensional quantum liquids, but disregards the high energy excitations.
The most important high energy excitations are holes which have infinite
lifetime at zero temperature. At finite temperatures they can be scattered by
thermally excited bosons. We describe the interaction of the hole with the
bosons by treating it as a mobile impurity in a Luttinger liquid. This approach
enables us to evaluate the scattering probability at arbitrary interaction
strength. In general, the result is expressed in terms of the hole spectrum,
its dependence on the density and momentum of the fluid, and the parameters of
the Luttinger liquid Hamiltonian. In the special case of Galilean invariant
systems the scattering probability is expressed in terms of only the hole
spectrum and its dependence on the fluid density. We apply our results to the
problem of equilibration of one-dimensional quantum liquids
Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
We consider zero temperature behavior of dynamic response functions of 1D
systems near edges of support in momentum-energy plane The
description of the singularities of dynamic response functions near an edge
is given by the effective Hamiltonian of a mobile impurity moving
in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters
of such an effective Hamiltonian to the properties of the function This allows us to express the exponents which characterize singular
response functions of spinless bosonic or fermionic liquids in terms of
and Luttinger liquid parameters for any For an
antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2)
invariance fixes the exponents from purely phenomenological considerations.Comment: final published versio
Exact diagonalisation of 1-d interacting spinless Fermions
We acquire a method of constructing an infinite set of exact eigenfunctions
of 1--d interacting spinless Fermionic systems. Creation and annihilation
operators for the interacting system are found and thereby the many--body
Hamiltonian is diagonalised. The formalism is applied to several examples. One
example is the theory of Jack polynomials. For the Calogero-Moser-Sutherland
Hamiltonian a direct proof is given that the asymptotic Bethe Ansatz is
correct.Comment: 33 page
Looking at the Haldane Conjecture from a Grouptheoretical Point of View
Based on the Lieb-Schultz-Mattis construction we present a five parameter
family of Spin-1 Hamiltonians with degenerate groundstate. Starting from the
critical symmetric Hamiltonian, we look for those perturbations of the
symmetry, which leave the groundstate degenerate. We also discuss the
spin-3/2 -case.Comment: 9 pages RevTex 3.
Non-conformal asymptotic behavior of the time-dependent field-field correlators of 1D anyons
The exact large time and distance behavior of the field-field correlators has
been computed for one-dimensional impenetrable anyons at finite temperatures.
The result reproduces known asymptotics for impenetrable bosons and free
fermions in the appropriate limits of the statistics parameter. The obtained
asymptotic behavior of the correlators is dominated by the singularity in the
spectral density of the quasiparticle states at the bottom of the band, and
differs from the predictions of the conformal field theory. One can argue,
however, that the anyonic response to the low-energy probes is still determined
by the conformal terms in the asymptotic expansion.Comment: 5 pages, RevTeX
A Note on Dressed S-Matrices in Models with Long-Range Interactions
The {\sl dressed} Scattering matrix describing scattering of quasiparticles
in various models with long-range interactions is evaluated by means of
Korepin's method\upref vek1/. For models with -interactions
the S-matrix is found to be a momentum-independent phase, which clearly
demonstrates the ideal gas character of the quasiparticles in such models. We
then determine S-matrices for some models with -interaction
and find them to be in general nontrivial. For the -limit of the
-interaction we recover trivial S-matrices, thus exhibiting
a crossover from interacting to noninteracting quasiparticles. The relation of
the S-matrix to fractional statistics is discussed.Comment: 18 pages, jyTeX (macro included - just TeX the file) BONN-TH-94-13,
revised version: analysis of models with 1/sinh^2 interaction adde
Exact Solution of Heisenberg-liquid models with long-range coupling
We present the exact solution of two Heisenberg-liquid models of particles
with arbitrary spin interacting via a hyperbolic long-range potential. In
one model the spin-spin coupling has the simple antiferromagnetic Heisenberg
exchange form, while for the other model the interaction is of the
ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz
equations of these models have a similar structure to that of the
Babujian-Takhatajan spin chain. We also conjecture the integrability of a third
new spin-lattice model with long-range interaction.Comment: 7pages Revte
Bunching Transitions on Vicinal Surfaces and Quantum N-mers
We study vicinal crystal surfaces with the terrace-step-kink model on a
discrete lattice. Including both a short-ranged attractive interaction and a
long-ranged repulsive interaction arising from elastic forces, we discover a
series of phases in which steps coalesce into bunches of n steps each. The
value of n varies with temperature and the ratio of short to long range
interaction strengths. We propose that the bunch phases have been observed in
very recent experiments on Si surfaces. Within the context of a mapping of the
model to a system of bosons on a 1D lattice, the bunch phases appear as quantum
n-mers.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let
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