Related papers: Bethe Ansatz, Quantum Circuits, and the F-basis
We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…
We present in this paper a comprehensive introduction to the algebraic Bethe Ansatz, taking as examples the six-vertex model with periodic and non-periodic boundary conditions. We propose a diagrammatic representation of the commutation…
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…
The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant…
Several studies have exploited the integrable structure of central spin models to deepen understanding of these fundamental systems. In recent years, an underlying supersymmetry for systems with XX interactions has been uncovered. Here we…
We propose a Bethe-Ansatz-type solution of the open spin-1/2 integrable XXZ quantum spin chain with general integrable boundary terms and bulk anisotropy values i \pi/(p+1), where p is a positive integer. All six boundary parameters are…
We study the trigonometric quantum spin-Calogero-Sutherland model, and the Haldane-Shastry spin chain as a special case, using a Bethe-ansatz analysis. We harness the model's Yangian symmetry to import the standard tools of integrability…
We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$ transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz.…
The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin…
Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…
We present the analytical Bethe ansatz for spin chains based on the superalgebras gl(M|N), $M\neq N$, with at each site an arbitrary representation (and including inhomogeneities). The calculation is done for closed and open spin chains. In…
We show that the quantum corrected string Bethe ansatz passes an important universality test by demonstrating that it correctly incorporates the non-analytical terms in the string sigma model one-loop correction for rational three-spin…
We investigate the exact overlaps between eigenstates of integrable spin chains and a special class of states called "integrable initial/final states". These states satisfy a special integrability constraint, and they are closely related to…
The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe…
We derive a criterion under which splitting of all eigenstates of an open $\XYZ$ Hamiltonian with boundary fields into two invariant subspaces, spanned by chiral shock states, occurs. The splitting is governed by an integer number, which…
We solve the $A_{2n}^{(2)}$ vertex model with all kinds of diagonal reflecting matrices by using the algebraic Behe ansatz, which includes constructing the multi-particle states and achieving the eigenvalue of the transfer matrix and…
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the…
Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$…
We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the…
Using the algebraic Bethe ansatz, we derive a matrix product representation of the exact Bethe-ansatz states of the six-vertex Heisenberg chain (either XXX or XXZ and spin-$\frac{1}{2}$) with open boundary conditions. In this…