The Completeness of the Bethe Ansatz for the Asymmetric Simple Exclusion Process

Fabian H. L. Eßler, Jan de Gier

Sylvain Prolhac

Fa-Kai Wen, Zhan-Ying Yang, Shuai Cui +2 more

We study the one-dimensional asymmetric simple exclusion process (ASEP) with generic open boundaries (including current-counting deformation), and obtain the exact solutions of this ASEP via the off-diagonal Bethe ansatz method. In particular, numerical results for the small size asymmetric simple exclusion process indicate that the spectrum obtained by the Bethe ansatz equations is complete. Moreover, we present the eigenvalue of the totally asymmetric exclusion process and the corresponding Bethe ansatz equations.

E. KOZAK, R. NIEMIEC, D. GOŁOJUCH +1 more

Xin Zhang, Fa-Kai Wen, Jan de Gier

Abstract We study the integrable two-species asymmetric simple exclusion process (ASEP) for two inequivalent types of open, non particle conserving boundary conditions. Employing the nested off-diagonal Bethe ansatz method, we construct for each case the corresponding homogeneous - relations and obtain the Bethe ansatz equations. Numerical checks for small system sizes show completeness for some Bethe ansatz equations, and partial completeness for others.

Nicolas Crampé, E. Ragoucy, Damien Simon

We present the construction of the full set of eigenvectors of the open asymmetric simple exclusion process (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 Ansatz specific to the ASEP. This 'matrix coordinate Bethe Ansatz' can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in the matrix Ansatz.