6,818 research outputs found
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
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
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
Density Correlation Functions in Calogero Sutherland Models
Using arguments from two dimensional Yang-Mills theory and the collective
coordinate formulation of the Calogero-Sutherland model, we conjecture the
dynamical density correlation function for coupling and , where is
an integer. We present overwhelming evidence that the conjecture is indeed
correct.Comment: 12 pages phyzzx, CERN-TH/94.7243 One reference change
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
Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons
We calculate the exact dynamical magnetic structure factor S(Q,E) in the
ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2
spinon excitations, the Haldane-Shastry model with inverse-square exchange,
which is in the same low-energy universality class as Bethe's nearest-neighbor
exchange model. Only two-spinon excited states contribute, and S(Q,E) is found
to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903
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.
Implementation of Spin Hamiltonians in Optical Lattices
We propose an optical lattice setup to investigate spin chains and ladders.
Electric and magnetic fields allow us to vary at will the coupling constants,
producing a variety of quantum phases including the Haldane phase, critical
phases, quantum dimers etc. Numerical simulations are presented showing how
ground states can be prepared adiabatically. We also propose ways to measure a
number of observables, like energy gap, staggered magnetization, end-chain
spins effects, spin correlations and the string order parameter
Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
We examine a collection of particles interacting with inverse-square two-body
potentials in the thermodynamic limit. We find explicit large-amplitude density
waves and soliton solutions for the motion of the system. Waves can be
constructed as coherent states of either solitons or phonons. Therefore, either
solitons or phonons can be considered as the fundamental excitations. The
generic wave is shown to correspond to a two-band state in the quantum
description of the system, while the limiting cases of solitons and phonons
correspond to particle and hole excitations.Comment: Version to appear in Physical Rerview Letters; contains some new
results and explanation
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