Related papers: Bethe Ansatz, Quantum Circuits, and the F-basis
We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state $\vert \Psi \rangle$ onto an optimal quantum circuit $\hat{\mathcal{C}}$ with a finite number of single- and two-qubit quantum gates. The proposed…
The exact solution of the one-dimensional super-symmetric t-J model under generic integrable boundary conditions is obtained via the Bethe ansatz methods. With the coordinate Bethe ansatz, the corresponding R-matrix and K-matrices are…
The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…
The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a…
We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix…
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic…
The thermodynamic Bethe ansatz (TBA) and the excited state TBA equations for an integrable spin chain related to the Lie superalgebra osp(1|2) are proposed by the quantum transfer matrix (QTM) method. We introduce the fusion hierarchy of…
It is known that for the Heisenberg XXZ spin-$\frac{1}{2}$ chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D…
We consider integrable boundary states in the XXX spin-1/2 spin chain. We begin by briefly reviewing the algebraic Bethe Ansatz as well as integrable boundary states in spin chains. Then a recently discovered class of integrable states…
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…
We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work…
The spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The…
In the paper arXiv:2002.12065, the authors developed a new method to compute the exact overlap formulas between integrable boundary states and on-shell Bethe states in integrable spin chains. This method utilizes the coordinate Bethe ansatz…
The coordinate Bethe ansatz solutions of the XXZ model for a one-dimensional spin-1/2 chain are analyzed with focus on the statistical properties of the constituent quasiparticles. Emphasis is given to the special cases known as XX, XXX,…
These are lecture notes of an introduction to quantum integrability given at the Tenth Modave Summer School in Mathematical Physics, 2014, aimed at PhD candidates and junior researchers in theoretical physics. We introduce spin chains and…
Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic,…
We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model.…
We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…
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…
The one-dimensional Hubbard model with arbitrary boundary magnetic fields is solved exactly via the Bethe ansatz methods. With the coordinate Bethe ansatz in the charge sector, the second eigenvalue problem associated with the spin sector…