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

TL;DR

This paper investigates the universal properties of dissipative Tomonaga-Luttinger liquids in a non-Hermitian XXZ spin chain, combining analytical and numerical methods to reveal how dissipation affects the system's universality class.

Contribution

It provides a comprehensive analysis of dissipative TL liquids using effective field theory, conformal field theory, Bethe-ansatz, and NH-DMRG, highlighting the impact of dissipation on universality and mass gap formation.

Findings

The massless regime with weak dissipation belongs to a complex-valued TL universality class.

Increasing dissipation causes the TL parameter to deviate, indicating a transition to a massive phase.

Results are relevant for ultracold atom systems with two-body loss, providing testable predictions.

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.