相关论文: A Q-operator for the quantum transfer matrix
We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to…
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of…
A proof is given that an invertible and a unitary operator can be used to reproduce the effect of a q-deformed commutator of annihilation and creation operators. In other words, the original annihilation and creation operators are mapped…
The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to the Yang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) for arbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtained in…
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…
Quantum singular value transformation (QSVT) enables the application of polynomial functions to the singular values of near arbitrary linear operators embedded in unitary transforms, and has been used to unify, simplify, and improve most…
We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an…
The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is…
We recognize quantum circuit model of computation as factorisable scattering model and propose that a quantum computer is associated with a quantum many-body system solved by the Bethe ansatz. As an typical example to support our…
The q-oscillator representation for the Borel subalgebra of the affine symmetry $U_q(sl_N^)$ is presented. By means of this q-oscillator representation, we give the free field realizations of the Baxter's Q-operator $Q_j(t)$, $\bar{Q}_j(t)$…
We introduce a two dimensional network of corner-sharing triangles with square lattice symmetry. Properties of magnetic systems here should be similar to those on the kagome lattice. Focusing on the spin half Heisenberg quantum…
We consider a unitary circuit where the underlying gates are chosen to be R-matrices satisfying the Yang-Baxter equation and correlation functions can be expressed through a transfer matrix formalism. These transfer matrices are no longer…
Q-operators for generalised eight vertex models associated to higher spin representations of the Sklyanin algebra are constructed by Baxter's first method and Fabricius's method, when the anisotropy parameter is rational.
The trigonometric su(n) spin chain with anti-periodic boundary condition (su(n) spin torus) is demonstrated to be Yang-Baxter integrable. Based on some intrinsic properties of the R-matrix, certain operator product identities of the…
The XXZ open spin chain with general integrable boundary conditions is shown to possess a q-deformed analogue of the Onsager's algebra as fundamental non-abelian symmetry which ensures the integrability of the model. This symmetry implies…
Non-manifest symmetries are an important feature of quantum field theories (QFTs), and yet their characteristics are not fully understood. In particular, the construction of the charge operators associated with these symmetries is…
We present a family of novel Lax operators corresponding to representations of the RTT-realisation of the Yangian associated with $D$-type Lie algebras. These Lax operators are of oscillator type, i.e. one space of the operators is…
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 propose Wronskian-like determinant formulae for the Baxter Q-functions and the eigenvalues of transfer matrices for spin chains related to the quantum affine superalgebra U_{q}(hat{gl}(M|N)). In contrast to the supersymmetric…
A generalization of the eight vertex model by means of higher spin representations of the Sklyanin algebra is investigated by the quantum inverse scattering method and the algebraic Bethe Ansatz. Under the well-known string hypothesis…