Transconducting Transition for a Dynamic Boundary Coupled to Several Tomonaga-Luttinger Liquids*

The question on how a quantum bath can affect the dynamical properties of a quantum degree of freedom is a long standing and important one.
Here we study a dynamic boundary, e.g., a mobile impurity, coupled to N independent Tomonaga-Luttinger liquids (TLLs) each with interaction parameter K.We demonstrate [1] that for N ≥ 2 there is a quantum phase transition at a critical value of K ≥ 1/2, where the TLL phases lock together at the particle position, resulting in a nonzero transconductance equal to e²/(Nh). We analyze this transition line and compare it with large N predictions. We discuss experimental applications both for cold atomic or condensed matter realizations.

[1] B. Horovitz, T. Giamarchi, and P. Le Doussal, Phys. Rev. Lett. 121, 166803 (2018)