Exact solution to the pairing equations for bosons in a one-dimensional model

Yupeng Wang, Fu‐Cho Pu

A one-dimensional boson - fermion model is considered. It is shown that the model is exactly solvable and the general Bethe eigenstates are constructed. On the basis of the Bethe ansatz equations, the ground state and the thermodynamics are also given in some closed integral equations.

A. S. Alexandrov

Daniel Charles Mattis, Élliott H. Lieb

Junpeng Cao, Yuzhu Jiang, Yupeng Wang

An exactly solvable model describing the low-density limit of the spin-1 bosons in a one-dimensional optical lattice is proposed. The exact Bethe ansatz solution shows that the low-energy physics of this system is described by a quantum liquid of spin singlet bound pairs. Motivated by the exact results, a mean-field approach to the corresponding three-dimensional system is carried out. Condensation of singlet pairs and coexistence with ordinary Bose-Einstein condensation are predicted.

Wenhua Hai, Guishu Chong, Qiongtao Xie

The mathematically exact solution of a one-dimensional (1D) quantum N-identical-boson system with zero-range pair interaction has been well known. We find that this solution is non-physical, since there exists a paradox of its energy expectation value, leading a basic contradiction to the mean-field theory of the system. A new integral equation that is equivalent to the corresponding Schrodinger one is established and its formally physical solution is derived. Energy correction from the average potential and harmonic waves of different momentums are demonstrated, and scattering amplitude of the physical solution and mean-field theory of the system are discussed.

Daniel Charles Mattis, Élliott H. Lieb