Related papers: An exact solution to asymptotic Bethe equation
The exact solution of an integrable anisotropic Heisenberg spin chain with nearest-neighbour, next-nearest-neighbour and scalar chirality couplings is studied, where the boundary condition is the antiperiodic one. The detailed construction…
We consider the fully anisotropic Heisenberg spin-1/2 antiferromagnet in a uniform magnetic field, whose ground-state is characterized by broken spin rotation symmetry and gapped spinon excitations. We expand on a recent mean-field approach…
We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of…
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.…
By using a set of gauge transformations, the exact solutions of the XXZ spin chain with unparallel boundary magnetic fields are derived in the framework of the algebraic Bethe ansatz. In the easy-plane case, we show the elementary…
We present the exact solution of a family of two-spins models. The models are solved by the algebraic Bethe ansatz method using the $gl(2)$-invariant $R$-matrix and a multi-spins Lax operator. The interactions are by the Heisenberg spins…
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.…
We construct the exact solution of a non-Hermitian $\mathscr{PT}$-symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that the system exhibits two types of phases we refer to as $A$ and $B$ phases. In the $B$…
Bethe ansatz solution of the two-axis two-spin Hamiltonian is derived based on the Jordan-Schwinger boson realization of the SU(2) algebra. It is shown that the solution of the Bethe ansatz equations can be obtained as zeros of the related…
We present the exact solution of the $Osp(1|2)$ invariant magnet by the Bethe ansatz approach. The associated Bethe ansatz equation exhibit a new feature by presenting an explicit and distinct phase behaviour in even and odd sectors of the…
A recently developed numerical method, entanglement perturbation theory (EPT), is used to study the antiferromagnetic Heisenberg spin chains with z-axis anisotropy $\lambda$ and magnetic field B. To demonstrate the accuracy, we first apply…
We prove that physical solutions to the Heisenberg spin chain Bethe ansatz equations are exactly obtained by imposing two zero-remainder conditions. This bridges the gap between different criteria, yielding an alternative proof of a…
We provide a conjecture for the following two quantities related with the spin-$\frac{1}{2}$ isotropic Heisenberg model defined over rings of even lengths: (i) the number of the solutions to the Bethe ansatz equations which correspond to…
Exact solutions of quantum lattice models serve as useful guides for interpreting physical phenomena in condensed matter systems. Prominent examples of integrability appear in one dimension, including the Heisenberg chain, where the Bethe…
We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin…
A new exactly solvable one-dimensional spin-3/2 Heisenberg model with SO(5)-invariance is proposed. The eigenvalues and Bethe ansatz equations of the model are obtained by using the nested algebraic Bethe ansatz approach. Several exotic…
We demonstrate the existence of special phantom excitations for open and periodically closed integrable systems at the example of the $XXZ$ Heisenberg spin chain. The phantom excitations do not contribute to the energy of the Bethe state…
Recently, the XXX spin chain with arbitrary boundary fields was successfully solved [1] via the off-diagonal Bethe ansatz method [2]. The correctness and the completeness of this solution were numerically verified by Nepomechie for one…
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,…
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-$1 \over 2$…