摘要: We discuss the description of generic excited states in quantum deformed AdS_5 x S^5 mirror thermodynamic Bethe ansatz and derive associated Y-system. This Y-system shows an interesting new feature; it depends explicitly on state under consideration. Similarly, also twisted boundary conditions. construct asymptotic solution these TBA equations by deriving transfer matrix for Hubbard model finding bound dressing phase. construction is insensitive to precise nature deformation, thereby provides a nontrivial check features which arise precisely at roots unity.