Bethe Ansatz Solutions and Excitation Gap of the Attractive Bose-Hubbard Model

The dynamics of many simple non-equilibrium systems are often studied through corresponding quantum Hamiltonians. Examples are the asymmetricXXZ chain Hamiltonian and the attractive Bose-Hubbard Hamiltonian for the single-step growth model [1] and the directed polymers in random media (DPRM) [2], respectively. The single-step growth model is a Kardar-Parisi-Zhang (KPZ) universality class growth model where the interface height h(x, t) grows in a stochastic manner under the condition that h(x± 1, t)− h(x, t) = ±1. The process is also called the asymmetric exclusion process (ASEP) in a different context. The evolution of the probability distribution for h(x, t) is generated by the asymmetric XXZ chain Hamiltonian [3]. The entire information about the dynamics is coded in the generating function e. Its time evolution, in turn, is given by the modified asymmetric XXZ chain Hamiltonian [4–6],