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

• URL: http://arxiv.org/abs/2112.12467v3
• Date: Thu, 19 May 2022 09:43:05 GMT
• Title: Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Authors: Kazuki Yamamoto, Masaya Nakagawa, Masaki Tezuka, Masahito Ueda, and Norio Kawakami
• Abstract summary: We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis. Our results can be tested with the two-component Bose-Hubbard system of ultracold atoms subject to two-body loss.
• Score: 3.4253416336476246
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 effective field theory with bosonization, finite-size scaling approach in conformal field theory, and the Bethe-ansatz solution. Our numerical analysis is based on the density-matrix renormalization group 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 begin to deviate from those obtained by the Bethe-ansatz analysis, indicating that the model becomes massive for strong dissipation. Our results can be tested with the two-component Bose-Hubbard system of ultracold atoms subject to two-body loss.

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