Related papers: Relativistic Calogero-Sutherland Model: Spin Gener…
Using the collective field technique, we give the description of the spin Calogero-Sutherland Model (CSM) in terms of free bosons. This approach can be applicable for arbitrary coupling constant and provides the bosonized Hamiltonian of the…
We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a model involving many unitary matrices. The resulting systems consist of particles on the circle with internal degrees of freedom, coupled…
Explicit-exact expressions for the particle propagator of the spin 1/2 Calogero-Sutherland model are derived for the system of a finite number of particles and for that in the thermodynamic limit. Derivation of the expression in the…
We derive a microscopic model describing the low-lying edge excitations in the fractional quantum Hall liquid with $\nu=\frac{\nu^*} {\tilde\phi\nu^*+1}$. For $\nu^*>0$, it is found that the composite fermion model reduces to an SU$(\nu^*)$…
We study the $q$-analogue of the Haldane-Shastry model, a partially isotropic (XXZ-like) long-range spin chain that enjoys quantum-affine (really: quantum-loop) symmetries at finite size. We derive the pairwise form of the Hamiltonian,…
The conformal limit over an anti-ferromagnetic vacuum of the fermionic spin $\frac{1}{2}$ Calogero-Sutherland Model is derived by using the wedge product formalism. The space of states in the conformal limit is identified with the Fock…
The $S=1/2$ Heisenberg antiferromagnet is studied on the kagom\'e lattice by using a Green's function method based on an appropriate decoupling of the equations of motion. Thermodynamic properties as well as spin-spin correlation functions…
The reductions of the free geodesic motion on a non-compact simple Lie group G based on the $G_+ \times G_+$ symmetry given by left- and right multiplications for a maximal compact subgroup $G_+ \subset G$ are investigated. At generic…
Universal scaling relations for dissipative Tomonaga-Luttinger (TL) liquids with SU($N$) spin symmetry are obtained for both fermions and bosons, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional…
We study the properties of the symplectic sp(2N) algebra deformed using Dunkl operators, which describe the dynamical symmetry of the generalized N-particle quantum Calogero model. It contains a symmetry subalgebra formed by the deformed…
We discuss the application of the method of the gaugeless Hamiltonian reduction to general relativity. This method is based on explicit resolving the global part of the energy constraint and on identification of one of the metric components…
The density-density correlation function of the Calogero-Sutherland model is represented as a Fourier transformation of the correlation function of bosonic exponents in the Gaussian model on a curved manifold.
The rational Calogero-Moser model of n one-dimensional quantum particles with inverse-square pairwise interactions (in a confining harmonic potential) is reduced along the radial coordinate of R^n to the `angular Calogero-Moser model' on…
Motivated by the concept of ideal mutual statistics, we study a multispecies Calogero-Sutherland model in which the interaction parameters and masses satisfy some specific relations. The ground state is exactly solvable if those relations…
Critical properties of the Calogero-Sutherland model of $BC_N$-type ($BC_N$-CS model) are studied. Using the asymptotic Bethe-ansatz spectrum of the $BC_N$-CS model, we calculate finite-size corrections in the energy spectrum. Since the…
We study new interactions between degrees of freedom for Calogero, Sutherland and confined Calogero spin models. These interactions are encoded by the generators of the Lie algebra so(N) or sp(N). We find the symmetry algebras of these new…
We construct the dynamical symmetry of the quantum Calogero model with particle exchange in a confining Coulomb field. This symmetry is governed by the algebra $so(N+1,2)$, deformed by exchange (Dunkl) operators, with its invariant sector…
We consider here the problem of a "central spin", with spin quantum number $S \gg 1$, interacting with a set of microscopic spins. Interactions between the microscopic spins are ignored. This model describes magnetic grains or magnetic…
We show that a particular many-matrix model gives rise, upon hamiltonian reduction, to a multidimensional version of the Calogero-Sutherland model and its spin generalizations. Some simple solutions of these models are demonstrated by…
Calogero-Sutherland models of type $BC_N$ are known to be relevant to the physics of one-dimensional quantum impurity effects. Here we represent certain correlation functions of these models in terms of generalized hypergeometric functions.…