Universal properties of dissipative Tomonaga-Luttinger liquids with SU(N) spin symmetry

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 with SU(N) spin symmetry, by using asymptotic Bethe-ansatz solutions and conformal field theory (CFT) in one-dimensional NH quantum many-body systems with SU(N) symmetry [1,2]. We uncover that the spectrum of dissipative TL liquids with SU(N) spin symmetry is described by the sum of one charge mode characterized by a complex generalization of c = 1 U(1) Gaussian CFT, and N −1 spin modes characterized by level-1 SU(N) Kac-Moody algebra with the conformal anomaly c = N −1, and thereby dissipation only affects the charge mode as a result of spin-charge separation in one-dimensional NH quantum systems. The derivation is based on a complex generalization of Haldane’s ideal-gas description, which is implemented by the SU(N) Calogero-Sutherland model with inverse-square long-range interactions.



[1] K. Yamamoto, M. Nakagawa, M. Tezuka, M. Ueda, and N. Kawakami, Phys. Rev. B 105, 205125 (2022)

[2] K. Yamamoto and N. Kawakami, arXiv:2207.04395.