Exactly Solvable Models of Deep Levels

A. A. Suzko, E. P. Velicheva

Tianhao Ren, I. L. Aleǐner

We developed a comprehensive semiclassical theory of solitons in one-dimensional systems at the BCS-BEC crossover to provide a semiclassical explanation of their excitation spectra. Our semiclassical results agree well with the exact solutions on both the deep BCS and the deep BEC side and explain qualitatively the smooth crossover between them. Especially, we showed that the minimum energy of the $S=1/2$ excitation is achieved exactly at the Fermi momentum ${k}_{F}=\ensuremath{\pi}n/2$, where $n{m}_{F}$ (${m}_{F}$ is the mass of the fermionic atom) is the total mass density of the system. This momentum remains unchanged along the whole crossover whether the mass is contained in the bosonic molecules as on the deep BEC side or in the fermionic atoms as on the deep BCS side. This phenomenon comes about as a result of a special feature of one-dimensional systems that the conventional quasiparticle is not stable with respect to soliton formation. It is valid not only in exactly solvable models, but also on the level of semiclassical theory. Besides, we also resolved the inconsistency of existing semiclassical theory with the exact solution of solitonlike $S=0$ excitations on the deep BCS side by a different proposal of soliton configuration.

Gerald Dennis Mahan

Boyka Aneva

Abstract We discuss the exact solvability of a lattice model with a flow within the matrix product ansatz to interacting many‐body systems from the point of view of a tridiagonal boundary algebra. It reveals deep symmetry properties of the multiparticle process which allow for the exact solution in the stationary state and puts the description of the dynamics into perspective.

Malte Henkel, Michel Pleimling