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

We demonstrate the universal properties of dissipative Tomonaga-Luttinger\n(TL) liquids by calculating correlation functions and performing finite-size\nscaling analysis of a non-Hermitian XXZ spin chain as a prototypical model in\none-dimensional open quantum many-body systems. Our analytic calculation is\nbased on effective field theory with bosonization, finite-size scaling approach\nin conformal field theory, and the Bethe-ansatz solution. Our numerical\nanalysis is based on the density-matrix renormalization group generalized to\nnon-Hermitian systems (NH-DMRG). We uncover that the model in the massless\nregime with weak dissipation belongs to the universality class characterized by\nthe complex-valued TL parameter, which is related to the complex generalization\nof the $c=1$ conformal field theory. As the dissipation strength increases, the\nvalues of the TL parameter obtained by the NH-DMRG begin to deviate from those\nobtained by the Bethe-ansatz analysis, indicating that the model becomes\nmassive for strong dissipation. Our results can be tested with the\ntwo-component Bose-Hubbard system of ultracold atoms subject to two-body loss.\n