Related papers: Spin operator matrix elements in the superintegrab…
We propose a tensor-network (TN) approach for solving classical optimization problems that is inspired by spectral filtering and sampling on quantum states. We first shift and scale an Ising Hamiltonian of the cost function so that all…
Transition operator method is proposed for description of the dynamics of spectroscopic transitions. Quantum-mechanical analogue of Landau-Lifshitz equation has been derived for the system representing itself the periodical…
We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators…
We propose that the Baxter $Q$-operator for the spin-1/2 XXZ quantum spin chain is given by the $j\to \infty$ limit of the transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. Applying this observation to the open…
We study the matrix ansatz in the quantum group framework, applying integrable systems techniques to statistical physics models. We start by reviewing the two approaches, and then show how one can use the former to get new insight on the…
Using the method of canonical group quantization, we construct the angular momentum operators associated to configuration spaces with the topology of (i) a sphere and (ii) a projective plane. In the first case, the obtained angular momentum…
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an…
Using the irreducible tensor-operator technique, we establish the relation between different forms of spin tomograms. Quantizer and dequantizer operators are presented in simple explicit forms and are specified for the low-spin states. The…
The efficiency of time dependent density matrix renormalization group methods is intrinsically connected with the rate of entanglement growth. We introduce a new measure of entanglement in the space of operators and show, for transverse…
We propose a convenient orthogonal basis of the Hilbert space for the Izergin-Korepin model (or the quantum spin chain associated with the $A^{(2)}_{2}$ algebra). It is shown that the monodromy-matrix elements acting on the basis take…
The algebraic structures underlying quasi-exact solvability for spin 1/2 Hamiltonians in one dimension are studied in detail. Necessary and sufficient conditions for a matrix second-order differential operator preserving a space of wave…
We present the two-mass QCD contributions to the polarized pure singlet operator matrix element at three loop order in $x$-space. These terms are relevant for calculating the polarized structure function $g_1(x,Q^2)$ at $O(\alpha_s^3)$ as…
Exact solution of the quantum integrable $D^{(2)}_2$ spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered…
Monodromy matrices of the $\tau_2$ model are known to satisfy a Yang--Baxter equation with a six-vertex $R$-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this…
In this article, we investigate systems of generalized Schr\"odinger operators and their fundamental matrices. More specifically, we establish the existence of such fundamental matrices and then prove sharp upper and lower exponential decay…
Matrix elements of spherical tensor operators are fundamental to the analysis of lanthanide spectra in both amorphous and crystalline host materials. In the intermediate coupling scheme, the eigenvectors of the Hamiltonian define the…
We establish dimerization in $O(n)$-invariant quantum spin chains with big enough $n$, in a large part of the phase diagram where this result is expected. This includes identifying two distinct ground states which are translations of one…
We develop a new method to compute the exact overlaps between integrable boundary states and on-shell Bethe states for integrable spin chains. Our method is based on the coordinate Bethe Ansatz and does not rely on the "rotation trick" of…
For the class of quantum integrable models generated from the $q-$Onsager algebra, a basis of bispectral multivariable $q-$orthogonal polynomials is exhibited. In a first part, it is shown that the multivariable Askey-Wilson polynomials…
We refine a method for finding a canonical form for symmetry operators of arbitrary order for the Schroedinger eigenvalue equation on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal…