Related papers: A Creation Operator for Spinons in One Dimension
In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shastry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonian and fractional statistics. The form factor…
We construct a semiclassical Schr\"{o}dinger operator such that the imaginary part of its resonances closest to the real axis changes by a term of size $h$ when a real compactly supported potential of size $o ( h )$ is added.
Motivated by field-theoretic predictions we investigate the stable excitations that exist in two characteristic gapped phases of a spin-1 model with Ising-like and single-ion anisotropies. The sine-Gordon theory indicates a region close to…
Partial wave amplitudes for production and decay of baryon resonances are constructed in the framework of the operator expansion method. The approach is fully relativistically invariant and allow us to perform combined analyses of different…
In our previous works on the XXZ chain of spin one half, we have studied the problem of constructing a basis of local operators whose members have simple vacuum expectation values. For this purpose a pair of fermionic creation operators…
In this paper we analyze deep inelastic one-particle inclusive processes for the case of spin-one targets or for the case of spin-one produced hadrons, such as rho mesons. This allows the measurement of new distribution and fragmentation…
We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this…
We study the thermodynamic properties of spin chains of Haldane-Shastry type associated with the A_{N-1} root system in the presence of a uniform external magnetic field. To this end, we exactly compute the partition function of these…
We analyze one-particle inclusive DIS in the case when a spin-1 hadron (such as a vector meson) is observed in the final state. We consider only leading order contributions in 1/Q, but we include transverse momentum of partons. Several new…
A theoretical formalism leading to elegant derivation of formulae for all spin observables is outlined for photo production of mesons with arbitrary spin parity $s^{\pi}$. The salient features of this formalism based on irreducible tensor…
The 1/$N$ expansion solutions for the interacting boson model are extended to higher orders using computer algebra. The analytic results are compared with those obtained from an exact diagonalization of the Hamiltonian and are shown to be…
IIt is shown that the celebrated Heun operator $H_e=-(a_0 x^3 + a_1 x^2 + a_2 x) \frac{d^2}{dx^2} + (b_0 x^2 + b_1 x + b_2)\frac{d}{dx} + c_0 x$ is the Hamiltonian of the $sl(2,R)$-quantum Euler-Arnold top of spin $\nu$ in a constant…
We theoretically study a spin Hamiltonian for spin-orbit-coupled ferromagnets on the honeycomb lattice. We find that the effective Hamiltonian for magnons, a quanta of spin-wave excitations from ordered states, is equivalent to the Haldane…
Multi-hadron operators are crucial for reliably extracting the masses of excited states lying above multi-hadron thresholds in lattice QCD Monte Carlo calculations. The construction of multi-hadron operators with significant coupling to the…
We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give the consistent operators for PN, PV, VN and NN scattering, where P, V and N denote pseudoscalar, vector and…
We use the spinor helicity formalism to calculate the cross section for production of three partons of a given polarization in Deep Inelastic Scattering (DIS) off proton and nucleus targets at small Bjorken x. The target proton or nucleus…
It is shown that, under some natural additional conditions, an operator which intertwines one cyclic singular unitary operator with one dimensional perturbation of another cyclic singular unitary operator is the operator of multiplication…
We study the thermodynamics and criticality of the su($m|n$) Haldane-Shastry chain of $BC_N$ type with a general chemical potential term. We first derive a complete description of the spectrum of this model in terms of $BC_N$-type motifs,…
We provide an intuitive understanding of the collective low-energy spin excitation of the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain, known as the spinon. To this end, we demonstrate how a single spinon can be excited by…
In this article we present comparisons between the spectrum of a one-dimensional Schr\"odinger operator for a particular periodic potential and for its restriction to a finite number of sites. We deduce from this finite, but large, number…