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 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.

23 pages, 7 figures, to appear in Phys. Rev. B

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Quantum trajectories and open many-body quantum systems
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• New Trends in Density Matrix Renormalization
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• Dissipation induced Tonks-Girardeau gas in an optical lattice
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Dissipation induced coherence of a two-mode Bose-Einstein condensate
• Entanglement Entropy of Non Unitary Conformal Field Theory
• Lieb-Liniger model of a dissipation-induced Tonks-Girardeau gas
• Correlations at PT-symmetric quantum critical point
• Ghost-spin chains, entanglement and $bc$-ghost CFTs
• A non-Hermitian critical point and the correlation length of strongly correlated quantum systems

Cited by in corpus (2)

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