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arXiv:2012.04628 · Physical Review Research

Luttinger liquid coupled to Ohmic-class environments

Andisheh Khedri, Antonio Štrkalj, Alessio Chiocchetta, Oded Zilberberg

Published Jul 9, 2021• 6 citations
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Abstract

The authors study the impact of various types of environments on the transport through a one dimensional interacting quantum wire, revealing that the inter-particle correlations can be engineered by the environment's noise statistic.
DOI
10.1103/physrevresearch.3.l032013

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We investigate the impact of noisy environments on transport through a one dimensional interacting quantum wire containing a scattering impurity. The impurity is known to induce a metal-insulator quantum phase transition as a function of the interaction strength in the wire. By considering Ohmic-class environments (ranging from Ohmic, to sub-Ohmic and super-Ohmic cases), we elucidate the influence of fluctuations on this phase transition. Within a perturbative renormalization group approach, we show that Ohmic environments keep the phase transition intact, while sub- and super-Ohmic environments, modify it into a smooth crossover at a scale that depends on the interaction strength in the wire. The system, however, still undergoes a metal-to-insulator-like transition when moving from sub-Ohmic to super-Ohmic environment noise. We further consider realistic experimental conditions due to finite length and finite temperatures of the wire, and explore the signatures of the phase transition in the temperature dependence of the impurity-induced back-scattering electrical conductance.
We revise a phase diagram for the sliding Luttinger liquid (SLL) of coupled one-dimensional quantum wires packed in two- or three-dimensional arrays in the absence of a magnetic field. We analyse whether physically justifiable (reasonable) inter-wire interactions, i.e. either the screened Coulomb or 'Coulomb-blockade' type interactions, stabilise the SLL phase. Calculating the scaling dimensions of the most relevant perturbations (the inter-wire single-particle hybridisation, charge-density wave, and superconducting inter-wire couplings), we find that their combination always destroys the SLL phase for the repulsive intra-wire interaction. However, suppressing the inter-wire tunnelling of repulsive fermions (when the charge-density wave is the only remaining perturbation), one can observe a stability region emerging due to the inter-wire forward scattering interaction.