Related papers: Classical facets of quantum integrability
A novel quantum-classical hybrid scheme is proposed to efficiently solve large-scale combinatorial optimization problems. The key concept is to introduce a Hamiltonian dynamics of the classical flux variables associated with the quantum…
We explore the space of solutions of the classical equations of motion in the Euclidean electroweak theory. We sketch a topological prescription that finds known solutions and indicates the existence of novel ones. All spatially-varying,…
A lattice model of interacting q-oscillators, proposed in [V. Bazhanov, S. Sergeev, arXiv:hep-th/0509181], is the quantum mechanical integrable model in 2+1 dimensional space-time. Its layer-to-layer transfer-matrix is a polynomial of two…
We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…
The quantum theory of the Liouville model with imaginary field is considered using the quantum inverse scattering method. An integrable structure with nontrivial spectral parameter dependence is developed for lattice Liouville theory by…
The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a…
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…
Exact quantum integrability is established for a class of multi-chain electron models with correlated hopping and spin models with interchain interactions, by constructing the related Lax operators and R-matrices through twisting and gauge…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
In this paper we consider affine Toda systems defined on the half-plane and study the issue of integrability, i.e. the construction of higher-spin conserved currents in the presence of a boundary perturbation. First at the classical level…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum…
Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without $U(1)$ symmetry, their spectra are usually given by inhomogeneous $T-Q$…
We consider the SU_q (N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between…
The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a…
We consider the generalized rotor Hamiltonians capable of describing quantum systems invariant with respect to symmetry point-groups that go beyond the usual D_2-symmetry of a tri-axial rotor. We discuss the canonical de-quantisation…
We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the…
Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries…
We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-invariant $R$-matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix.…
The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in…
We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the…