Related papers: Exact Solution of Long-Range Interacting Spin Chai…
In this paper we consider two a priori very different problems: construction of the eigenstates of the spin chains with non parallel boundary magnetic fields and computation of the partition function for the trigonometric solid-on-solid…
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 consider two-site XXX Heisenberg magnets with different boundary conditions, which are integrable systems on so(4) possessing additional cubic and quartic integrals of motion. The separated variables for these models are constructed…
We study integrable models for electrons in metals when the single particle spectrum is discrete. The electron-electron interactions are BCS-like pairing, Coulomb repulsion, and spin exchange coupling. These couplings are, in general,…
For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice can be used to compute the ground state wave function and the dynamical…
We consider the most general three-state spin chain with U(1)^3 symmetry and nearest neighbour interaction. Our model contains as a special case the spin chain describing the holomorphic three scalar sector of the three parameter complex…
In this work we study scalar products of Bethe vectors associated with the $XXZ$ spin chain with open boundary conditions. The scalar products are obtained as solutions of a system of functional equations. The description of scalar products…
Quantum spin chains arise naturally from perturbative large-N field theories and matrix models. The Hamiltonian of such a model is a long-range deformation of nearest-neighbor type interactions. Here, we study the most general long-range…
We generalize the SU(2|2) supersymmetric extended Hubbard model of 1/r2 interaction to the SU(m|n) supersymmetric case. Integrable models may be defined on both uniform lattice and non-uniform one dimensional lattices. We study both cases…
The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector…
We introduce a class of exactly solvable boson models. We give explicit analytic expressions for energy eigenvalues and eigenvectors for an sd-boson Hamiltonian, which is related to the SO(6) chain of the Interacting Boson Model…
Integrable boundary conditions are studied for critical A-D-E and general graph-based lattice models of statistical mechanics. In particular, using techniques associated with the Temperley-Lieb algebra and fusion, a set of boundary…
An infinite number of solvable Hamiltonians, including the transverse Ising chain, the XY chain with an external field, the cluster model with next-nearest-neighbor x-x interactions, or with next-nearest-neighbor z-z interactions, and other…
Two types of boundary conditions ("soliton preserving" and "soliton non-preserving") are investigated for the sl(n) and sl(m|n) open spin chains. The appropriate reflection equations are formulated and the corresponding solutions are…
The Hamiltonian symmetry reduction of the geodesics system on a symmetric space of negative curvature by the maximal compact subgroup of the isometry group is investigated at an arbitrary value of the momentum map. Restricting to regular…
Considering a spin-up and a spin-down fermion in a generic tight-binding lattice with a multi-site basis, we investigate the two-body problem using a multiband extended-Hubbard model with finite-ranged hopping and interaction parameters. We…
We prove the Lieb-Schultz-Mattis theorem in $d$-dimensional spin systems exhibiting $SO(3)$ spin rotation and lattice translation symmetries in the presence of $k-$local interactions decaying as $\sim 1/r^\alpha$ with distance $r$. Two…
By taking the freezing limit of a spin Calogero-Sutherland model containing `anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This…
We define a monodromy, directly from the spectrum of small non-selfadjoint perturbations of a selfadjoint semiclassical operator with two degrees of freedom, which is classically integrable. It is a combinatorial invariant that obstructs…
The reflection equations in a $su(3)$ spin chain with open boundary conditions are analyzed. We find non diagonal solutions to the boundary matrices. The corresponding hamiltonian is given. The solutions are generalized to $su(n)$.