Universal properties of dissipative Tomonaga-Luttinger liquids

In recent years, open quantum systems have been actively studied both experimentally and theoretically, as exemplified by driven-dissipative systems and non-Hermitian (NH) quantum systems. In this talk, we demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by deriving correlation functions and performing finite-size scaling analysis for a NH XXZ spin chain as a prototypical correlated model in one-dimensional open quantum systems [1]. Our calculation is based analytically on the field theory, the finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution, and numerically on the density-matrix renormalization group analysis generalized to NH systems (NH-DMRG). Importantly, we uncover that the model belongs to the universality class characterized by the complex-valued TL parameter in the massless regime with weak dissipation. On the other hand, the discrepancy in the TL parameter obtained by NH-DMRG and the Bethe-ansatz analysis indicates that the model becomes massive for strong dissipation. Our results can be tested in ultracold atoms by introducing two-body loss to the Bose-Hubbard model with photoassociation techniques [2].

[1] K. Yamamoto et al., to be submitted.

[2] T. Tomita et al., Sci. Adv. 3, e1701513 (2017).