Related papers: Correlations and commuting transfer matrices in in…
We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They…
We determine the eigenvalues of the transfer matrices for integrable open quantum spin chains which are associated with the affine Lie algebras $A^{(2)}_{2n-1}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n$, and which have the quantum-algebra invariance…
Critical site percolation on the triangular lattice is described by the Yang-Baxter solvable dilute $A_2^{(2)}$ loop model with crossing parameter specialized to $\lambda=\frac\pi3$, corresponding to the contractible loop fugacity…
Introducing a class of SU(2) invariant quantum unitary circuits generating chiral transport, we examine the role of broken space-reflection and time-reversal symmetries on spin transport properties. Upon adjusting parameters of local…
We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…
We present a supermatrix realisation of q-deformed spinor-spinor and spinor-vector R-matrices. These R-matrices are then used to construct transfer matrices for $U_{q^2}(\mathfrak{so}_{2n+1})$- and $U_{q}(\mathfrak{so}_{2n+2})$-symmetric…
Using the Algebraic Bethe Ansatz we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin $\frac 12$ Heisenberg chain, based on the solution of the quantum inverse…
The hierarchy of commuting maps related to a set-theoretical solution of the quantum Yang-Baxter equation (Yang-Baxter map) is introduced. They can be considered as dynamical analogues of the monodromy and/or transfer-matrices. The general…
For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum…
We investigate the relation between integrability and decoherence in central spin models with more than one central spin. We show that there is a transition between integrability ensured by the Bethe ansatz and integrability ensured by…
We formulate correlation functions for a one-dimensional interacting spinless fermion model at finite temperature. By combination of a lattice path integral formulation for thermodynamics with the algebraic Bethe ansatz for fermion systems,…
Inspired by the integrable structures appearing in weakly coupled planar N=4 super Yang-Mills theory, we study Q-operators and Yangian invariants of rational integrable spin chains. We review the quantum inverse scattering method along with…
In [1] an integrable quantum model was introduced and a class of its cyclic representations was proven to define lattice regularizations of the Sine-Gordon model. Here, we analyze general cyclic representations of this integrable quantum…
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…
Quantum circuits with gates (local unitaries) respecting a global symmetry have broad applications in quantum information science and related fields, such as condensed matter theory and quantum thermodynamics. However, despite their…
We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to…
Quantum dynamics with local interactions in lattice models display rich physics, but is notoriously hard to study. Dual-unitary circuits allow for exact answers to interesting physical questions in clean or disordered one- and…
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian Y(sl(3)) on Bethe vectors are considered. These…
We consider the XXZ spin chain with diagonal boundary conditions in the framework of algebraic Bethe Ansatz. Using the explicit computation of the scalar products of Bethe states and a revisited version of the bulk inverse problem, we…
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…