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

Abstract

We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis of a non-Hermitian XXZ spin chain as a prototypical model in one-dimensional open quantum many-body systems. Our analytic calculation is based on an effective field theory with bosonization, a finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution. We also perform numerical calculations based on the density-matrix renormalization group analysis generalized to non-Hermitian systems (NH-DMRG). We uncover that the model in the massless regime with weak dissipation belongs to the universality class characterized by the complex-valued TL parameter, which is related to the complex generalization of the c = 1 conformal field theory. As the dissipation strength increases, the values of the TL parameter obtained by the NH-DMRG and the Bethe-ansatz analysis start to deviate from each other, indicating that the model becomes massive for strong dissipation. Our results can be tested with ultracold atoms by introducing two-body loss to the two-component Bose-Hubbard system.