A simple derivation of the higher-level Bethe ansatz equations

L.V. Avdeev, Alexey A. Vladimirov

Xin Zhang, Fa-Kai Wen

We study the asymmetric simple exclusion process with nondiagonal 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 state is presented. Using the coordinate Bethe ansatz method, we derive a concise expression for the steady state. The current and density profile in the steady state are also studied.

N. A. Slavnov

N. Cirilo António, N. Manojlović, Igor Salom

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

O. Golinelli, Kirone Mallick

We present a new derivation of the spectral gap of the totally asymmetric exclusion process on a half-filled ring of size L by using the Bethe ansatz. We show that, in the large- L limit, the Bethe equations reduce to a simple transcendental equation involving the polylogarithm, a classical special function. By solving that equation, the gap and the dynamical exponent are readily obtained. Our method can be extended to a system with an arbitrary density of particles.