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We demonstrate the universal properties of dissipative Tomonaga-Luttinger(TL) liquids by calculating correlation functions and performing finite-sizescaling analysis of a non-Hermitian XXZ spin chain as a prototypical model inone-dimensional open quantum many-body systems. Our analytic calculation isbased on effective field theory with bosonization, finite-size scaling approachin conformal field theory, and the Bethe-ansatz solution. Our numericalanalysis is based on the density-matrix renormalization group generalized tonon-Hermitian systems (NH-DMRG). We uncover that the model in the masslessregime with weak dissipation belongs to the universality class characterized bythe complex-valued TL parameter, which is related to the complex generalizationof the $c=1$ conformal field theory. As the dissipation strength increases, thevalues of the TL parameter obtained by the NH-DMRG begin to deviate from thoseobtained by the Bethe-ansatz analysis, indicating that the model becomesmassive for strong dissipation. Our results can be tested with thetwo-component Bose-Hubbard system of ultracold atoms subject to two-body loss.

Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain