In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of
the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian …

We present a family of exactly solvable generalizations of the Jaynes-Cummings model
involving the interaction of an ensemble of SU (2) or SU (1, 1) quasispins with a single …

We study the exact solution for a two-mode model describing coherent coupling between
atomic and molecular Bose–Einstein condensates (BEC), in the context of the Bethe ansatz …

The concept of quantum integrability has been introduced recently for quantum systems with
explicitly time-dependent Hamiltonians (Sinitsyn et al 2018 Phys. Rev. Lett. 120 190402) …

We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations
of the Yang–Baxter algebra. The main deviation from the standard approach consists in a …

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the
Tavis-Cummings Hamiltonian, based on polynomially deformed su (2), ie, su n (2) algebras …

We introduce the anisotropic two-photon Rabi model in which the rotating and counter
rotating terms enters the Hamiltonian with two different coupling constants. Eigenvalues and …

We construct commuting transfer matrices for models describing the interaction between a
single quantum spin and a single bosonic mode using the quantum inverse scattering …

We obtain the exact solutions for a family of spin-boson systems. This is achieved through
application of the representation theory for polynomial deformations of the su (2) Lie …

The influence of the dynamical Stark shift on the thermal entanglement and the efficiency of
the quantum Otto cycle is studied for the su (1, 1) Tavis–Cummings system. It is shown that …