T(T)over-bar-deformed 1d Bose gas

T (T) over bar deformation was originally proposed as an irrelevant solvable deformation for 2d relativistic quantum field theories (QFTs). The same family of deformations can also be defined for integrable quantum spin chains which was first studied in the context of integrability in AdS/CFT. In this paper, we construct such deformations for yet another type of models, which describe a collection of particles moving in 1d and interacting in an integrable manner. The prototype of such models is the Lieb-Liniger model. This shows that such deformations can be defined for a very wide range of systems. We study the finite volume spectrum and thermodynamics of the T (T) over bar -deformed Lieb-Liniger model. We find that for one sign of the deformation parameter (lambda < 0), the deformed spectrum becomes complex when the volume of the system is smaller than certain critical value, signifying the break down of UV physics. For the other sign (lambda > 0), there exists an upper bound for the temperature, similar to the Hagedorn behavior of the T (T) over bar -deformed QFTs. Both behaviors can be attributed to the fact that T (T) over tilde -deformation changes the size the particles. We show that for lambda > 0, the deformation increases the spaces between particles which effectively increases the volume of the system. For lambda < 0, T<(T)over bar>-deformation fattens point particles to finite size hard rods. This is similar to the observation that the action of T (T) over bar -deformed free boson is the Nambu-Goto action, which describes bosonic strings-also an extended object with finite size.

Automated summary

This paper studies the finite volume spectrum and thermodynamics of the T(T) over bar-deformed Lieb-Liniger model. The results show that when the volume is smaller than a critical value, the deformed spectrum becomes complex, indicating the breakdown of UV physics for one sign of the deformation parameter. For the other sign, there exists an upper bound for the temperature, similar to the Hagedorn behavior of the T(T) over bar-deformed QFTs. Both behaviors can be attributed to the change in particle size caused by the T(T) over tilde-deformation.