Related papers: On Integrable Quantum Group Invariant Antiferromag…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…
We construct new families of spin chain Hamiltonians that are local, integrable and translationally invariant. To do so, we make use of the Clifford group that arises in quantum information theory. We consider translation invariant Clifford…
Integrable Hamiltonians for higher spin periodic XXZ chains are constructed in terms of the spin generators; explicit examples for spins up to 3/2 are given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and U(1)-symmetric…
We show that the quantum-algebra-invariant open spin chains associated with the affine Lie algebras $A^{(1)}_n$ for $n>1$ are integrable. The argument, which applies to a large class of other quantum-algebra-invariant chains, does not…
We construct a pivotal category by a finite presentation and show that it is an integral form of the category of invariant tensors of the spin representation of the quantum group U_q(B_3) over the field of rational functions in q.
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
Using anisotropic R-matrices associated with affine Lie algebras $\hat g$ (specifically, $A_{2n}^{(2)}, A_{2n-1}^{(2)}, B_n^{(1)}, C_n^{(1)}, D_n^{(1)}$) and suitable corresponding K-matrices, we construct families of integrable open…
We introduce a new family of integrable theories with $N$ bosons and $N$ freely adjustable mass parameters. These theories restrict in particular limits to the ``generalized supersymmetric'' sine-Gordon models, as well as to the flavor…
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…
The centrally extended superalgebra psu(2|2)xR^3 was shown to play an important role for the integrable structures of the one-dimensional Hubbard model and of the planar AdS/CFT correspondence. Here we consider its quantum deformation…
We show that the anisotropic Heisenberg-Ising chains with higher spin allow, for special values of the anisotropy, integrable deformations intimately related to the theory of quantum groups at roots of unity. For the spin one case we…
We construct the family of spin chain Hamiltonians, which have affine quantum group symmetry. Their eigenvalues coincide with the eigenvalues of the usual spin chain Hamiltonians, but have the degeneracy of levels, corresponding to affine…
A countable set of quantum superintegrable systems for arbitrary spin is solved explicitly using tools of supersymmetric quantum mechanics. It is shown that these systems (introduced by Pronko, J. Phys. A: Math. Theor. 40 (2007) ) include…
We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…
We consider the integrable spin chain model - the noncompact SL(2,R) spin magnet. The spin operators are realized as the generators of the unitary principal series representation of the SL(2,R) group. In an explicit form, we construct…
We refine the recently introduced notion of eclectic spin chains by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians.…
The paper is devoted to the problem of finding free generators in the fields of invariants for actions of unipotent groups on affine varieties. We consider the case when the unipotent group is the unipotent radical in an arbitrary parabolic…
We discuss a class of transfer matrix built by a particular combination of isomorphic and non-isomorphic GL(N) invariant vertex operators. We construct a conformally invariant magnet constituted of an alternating mixture of GL(N) ``spins''…
A family of classical integrable systems defined on a deformation of the two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed through Hamiltonians defined on the non-standard quantum deformation of a sl(2) Poisson…