Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid

Abstract

Non-Hermitian physics in open quantum many-body systems provides novel opportunities for the discovery of exotic quantum phenomena unexpected in Hermitian systems. A previous study of the non-Hermitian Kondo problem in ultracold atoms reports reversion of renormalization group flows which violates the $g$ theorem and produces an unusual quantum phase transition. In this work, we study the effect of electron-electron interactions by considering the non-Hermitian Kondo problem in a Luttinger liquid. By performing a perturbative renormalization group analysis to two-loop order, we find that the interplay between non-Hermitian Kondo couplings and electron-electron interactions can produce a pair of complex fixed points. Complex fixed points have often been discussed in an attempt to understand the extremely long correlation length of Hermitian systems with weakly first-order transitions. Here, we show that complex fixed points arise naturally and can be physically realized in open quantum systems. We discuss consequences of the complex fixed points and future directions.

7+5 pages, 3 figures, 1 table

References in corpus (8)

• Quantum trajectories and open many-body quantum systems
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain
• Quantum-gas microscopes - A new tool for cold-atom quantum simulators
• Universal description of dissipative Tomonaga-Luttinger liquids with SU($N$) spin symmetry: Exact spectrum and critical exponents
• Non-Fermi liquid behavior and quantum criticality in cubic heavy fermion systems with non-Kramers multipolar local moments

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