Abstract
In the paper [1], the authors developed a new method to compute the exact overlap formulas between integrable boundary states and on-shell Bethe states in integrable spin chains. This method utilizes the coordinate Bethe ansatz representation of wave functions and singularity property of the off-shell overlaps. In this paper, we use this new method to derive the formula for overlaps between the Lieb-Liniger Bethe states and the Bose-Einstein condensate (BEC) state. As a simple application this method, we obtained the overlaps between the Lieb-Liniger eigenstates and the free particle states with pair structure.
Highlights
In the paper [1], the authors developed a new method to compute the exact overlap formulas between integrable boundary states and on-shell Bethe states in integrable spin chains
In a very recent paper [1], the author proposed a new method to directly calculate the overlap between on-shell Bethe states and integrable states in integrable spin chain models using the Coordinate Bethe Ansatz (CBA) formalism
We use this newly proposed method to derive the overlap for the Bose-Einstein condensate (BEC) state with the Lieb-Liniger energy eigenstate, which agrees with the early result
Summary
We consider one-dimensional Boson gas on a ring of circumference L with δ-function repulsive potential and impose periodic boundary condition. This is the famous Lieb-Liniger model, whose Hamiltonian is given by. We will set 2m = = 1 in the following for simplicity
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