Related papers: Yangian-invariant spin models and Fibonacci number…
The Yangian symmetry Y(su($n$)) of the Calogero-Sutherland-Moser spin model is reconsidered. The Yangian generators are constructed from two non-commuting su($n$)-loop algebras. The latters generate an infinite dimensional symmetry algebra…
We provide a rigorous proof of the fact that the level density of all su(m) spin chains of Haldane-Shastry type associated with the A_{N-1} root system approaches a Gaussian distribution as the number of spins N tends to infinity. Our…
We review the spin bit model describing anomalous dimensions of the operators of Super Yang--Mills theory. We concentrate here on the scalar sector. In the limit of large $N$ this model coincides with integrable spin chain while at finite N…
We study multi-hadron systems with a single heavy quark (charm or bottom) in the limit of heavy quark mass. The spin degeneracy of the states with quantum numbers $(j+1/2)^{P}$ and $(j-1/2)^{P}$ for $j \neq 0$, known in a normal hadron, can…
We study the open version of the su$(m|n)$ supersymmetric Haldane-Shastry spin chain associated to the $BC_N$ extended root system. We first evaluate the model's partition function by modding out the dynamical degrees of freedom of the…
Recently, the one dimensional model of $N$ spins with $S=\frac{1}{2}$ on a circle, interacting with an exchange that falls off with the inverse square of the separation: $H_{\rm ISE} =\sum_{i\neq j} \frac{1}{[\frac{N}{\pi}…
In a recent paper (cond-mat/0009279), Fabricius and McCoy studied the spectrum of the spin 1/2 XXZ-model at Delta = (q+q^{-1})/2 and q^{2N}=1 for integer N >1. They found a certain pattern of degeneracies and linked it to the sl(2)-loop…
We study the $\mathfrak{gl}_{1|1}$ supersymmetric XXX spin chains. We give an explicit description of the algebra of Hamiltonians acting on any cyclic tensor products of polynomial evaluation $\mathfrak{gl}_{1|1}$ Yangian modules. It…
The one-dimensional Hubbard model is an exceptional integrable spin chain which is apparently based on a deformation of the Yangian for the superalgebra gl(2|2). Here we investigate the quantum-deformation of the Hubbard model in the…
In the quantized two-dimensional non-linear supersymmetric $\sigma$-model, the supercurrent supermultiplet, which contains the energy-momentum tensor, is transformed by the nonlocal symmetry of the model into the isospin current…
The spectral decomposition of the path space of the vertex model associated to the vector representation of the quantized affine algebra $U_q(\hat{sl}_n)$ is studied. We give a one-to-one correspondence between the spin configurations and…
The $\gamma_i$-deformed $\mathcal{N}=4$ super-Yang-Mills theory is a non-supersymmetric deformation of the maximally-supersymmetric gauge theory in four dimensions which is conformally-invariant at the planar level. At the non-planar level…
The anomalous dimensions of local single trace gauge invariant operators in N=4 supersymmetric Yang-Mills theory can be computed by diagonalizing a long range integrable Hamiltonian by means of perturbative asymptotic Bethe ansatz. This…
We present an analysis of the Yangian symmetries of various bosonic sectors of the dilatation operator of $\cal N$$=4$ SYM. The analysis is presented from the point of view of Hamiltonian matrix models. In the various SU(n) sectors, we give…
We compute the spectrum of the su(m) spin Sutherland model of B_N type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the…
We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial ("identity") channel,…
The maximally supersymmetric Yang-Mills theory in four-dimensional Minkowski space is an exceptional model of mathematical physics. Even more so in the planar limit, where the theory is believed to be integrable. In particular, the…
This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane--Shastry model obey abelian half-fermi statistics,…
Various aspects of the Haldane-Shastry spin chain with 1/r^2 exchange, and its various generalizations, are reviewed, with emphasis on its Yangian quantum group structure, and the interpretation of the model as the generalization of an…
It is well known through a recent work of Bernard, Gaudin, Haldane and Pasquier (BGHP) that the usual spin Calogero-Sutherland (CS) model, containing particles with $M$ internal degrees of freedom, respects the $Y(gl_M)$ Yangian symmetry.…