Related papers: Boundary two-parameter eight-state supersymmetric …
We report a bound state of the one-dimensional two-particle (bosonic or fermionic) Hubbard model with an impurity potential. This state has the Bethe-ansatz form, although the model is nonintegrable. Moreover, for a wide region in parameter…
We study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by…
We study the generalized supersymmetric t-J model with Kondo impurities in the boundaries. We first construct the higher spin operator K-matrix for the XXZ Heisenberg chain. Setting the boundary parameter to be a special value, we find a…
We consider a model of strongly correlated electrons in 1D called the t-J model, which was solved by graded algebraic Bethe ansatz. We use it to design graded tensor networks which can be contracted approximately to obtain a Matrix Product…
Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula.…
The coupled Bethe--Salpeter bound state equations for a $Q\bar Q$ system, where $Q=(U,D)$ is a degenerate, fourth generation, super--heavy quark doublet, are solved in several ladder approximation models. The exchanges of gluon, Higgs and…
The formulation and resolution of integrable lattice statistical models in a quantum group covariant way is the subject of this review. The Bethe Ansatz turns to be remarkably useful to implement quantum group symmetries and to provide…
Much use has been made of the techniques of supersymmetric quantum mechanics (SUSY QM) for studying bound-state problems characterized by a superpotential $\phi(x)$. Under the analytic continuation $\phi(x) \to i\phi(x)$, a pair of…
We introduce a new unconditionally solvable level-crossing two-state model given by a constant-amplitude optical field configuration for which the detuning is an inverse-square-root function of time. This is a member of one of the five…
We discuss formulations of boundary conditions in a quantum graph vertex and demonstrate that the so-called $ST$-form can be further reduced up to a form more effective in certain applications: In particular, in identifying the number of…
We study the asymmetric simple exclusion process with non-diagonal boundary terms under a specific constraint. A symmetric chiral basis is constructed and a special string solution of the Bethe ansatz equations corresponding to the steady…
The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation. [S. Bravyi and D. Gosset, Comm. Math. Phys. 356, 451 (2017)]. It is…
$Z_n$ Belavin model with open boundary condition is studied. The double-row transfer matrices of the model are diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the face-vertex correspondence relation. The…
We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using…
A non-covariant but approximately relativistic two-body wave equation (Breit equation) describing the quantum mechanics of two fermions interacting with one another through a potential containing scalar, pseudoscalar and vector parts is…
Various versions of the Bethe ansatz are suggested for evaluation of scattering two-magnon states in 2D and 3D Heisenberg-Ising ferromagnets. It is shown that for 2D square (3D qubic) finite-periodic or infinite lattices about a half (3/4)…
A new method for describing the two-level pairing model in a many-fermion system is presented. Basic idea comes from the Schwinger boson representation for the su(2) cross su(2)-algebra, in which four kinds of boson operators govern the…
The Bethe-Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic Quantum Field Theory. Nevertheless a thorough discussion how to identify its solutions with physical states is…
We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical…
Boundary conditions compatible with integrability are obtained for two dimensional models by solving the factorizability equations for the reflection matrices $K^{\pm}(\theta)$. For the six vertex model the general solution depending on…