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arXiv:2105.01059 · Physical review. B./Physical review. B

Shape effects of localized losses in quantum wires: Dissipative resonances and nonequilibrium universality

Thomas Müller, Marcel Gievers, Heinrich Fröml, Sebastian Diehl, Alessio Chiocchetta

Published Oct 26, 2021• 23 citations
arXivHTMLPDF

Abstract

The authors study the role of the shape of dissipative impurities in quantum wires of ultracold atoms and predict a variety of resonance effects at the single-particle level. The interplay between interactions and dissipative impurities of finite width is further analyzed. In the case of attractive interactions, a line of renormalization-group fixed points emerges, showing that non-Hermiticity induces a novel kind of universality compared to the Hermitian counterpart.

DOI
10.1103/physrevb.104.155431

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The authors study the role of the shape of dissipative impurities in quantum wires of ultracold atoms and predict a variety of resonance effects at the single-particle level. The interplay between interactions and dissipative impurities of finite width is further analyzed. In the case of attractive interactions, a line of renormalization-group fixed points emerges, showing that non-Hermiticity induces a novel kind of universality compared to the Hermitian counterpart.
The effect of localized loss on a one-dimensional gas of interacting fermions is investigated. Here, the interplay of gapless quantum fluctuations and particle interactions strongly renormalizes the dissipative impurity. As a result, the loss probability for modes close to the Fermi energy vanishes for arbitrary strength of the dissipation, as a many-body incarnation of the quantum Zeno effect. This is reflected in the shape of the particle momentum distribution, exhibiting a peak close to the Fermi momentum.
We use the nonequilibrium Green's function formalism and a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire. We study how the conductance varies with the wire length, the temperature, and the strengths of the impurity and interactions. The numerical results for the dependence of the conductance on the wire length and temperature are compared with the results obtained from a renormalization group analysis based on the Hartree-Fock approximation. For the spin-1∕21∕21∕2 model with a repulsive on-site interaction or the spinless model with an attractive nearest neighbor interaction, we find that the conductance increases with increasing wire length or decreasing temperature. This can be explained using the Born approximation in scattering theory. For a strong impurity, the conductance is significantly different for a repulsive and an attractive impurity; this is due to the existence of a bound state in the latter case. In general, the large density deviations close to the impurity have an appreciable effect on the conductance at short distances which is not captured by the renormalization group equations.
We investigate the transport properties of a quantum wire of weakly interacting fermions in the presence of local particle loss. We calculate current and conductance in this system due to applied external chemical potential bias that can be measured in experimental realizations of ultracold fermions in quasi one-dimensional traps. Using a Keldysh field theory approach based on the Lindblad equation, we establish a perturbative scheme to study the effect of imbalanced reservoirs. Logarithmically divergent terms are resummed using a renormalization group method, and a novel powerlaw behavior for the conductance as a function of the potential bias across the wire is found. In contrast to the equilibrium case of a potential barrier in a Luttinger liquid, the conductance exhibits a scaling behavior, which depends on the interaction strength and on the loss probability. Repulsive interactions reduce the conductance of the wire while attractive interactions enhance it. However, perfect reflectivity and transparency are only reached in the absence of particle loss. Published by the American Physical Society 2024
Motivated by the realization of a dissipative quantum point contact in ultracold atomic gases, we investigate a two-terminal mesoscopic transport system in which a single-particle loss is locally present in a one-dimensional chain. By means of the Dyson equation approach in the Keldysh formalism that can incorporate dissipative effects, we reveal analytic structures of the particle and energy currents whose formal expressions correspond to ones in certain three-terminal systems where particle loss is absent. The obtained formulas are also consistent with non-Hermitian and three-terminal Landauer-B\"uttiker analyses. The universality of the current expressions holds regardless of the quantum statistics, and may be useful for understanding lossy two-terminal transport in terms of three-terminal transport and vice versa.
We analyze the competition between strong correlations and dissipation in quantum impurity systems from the Kondo regime to the valence fluctuation regime by developing a slave-boson theory for a non-Hermitian Anderson impurity model with one-body loss. Notably, in the non-Hermitian Kondo regime, strong correlations qualitatively change the nature of dissipation through renormalization effects, where the effective one-body loss is suppressed and emergent many-body dissipation characterized by the complex-valued hybridization is generated. We unveil the mechanism of a dissipative quantum phase transition of the Kondo state on the basis of this renormalization effect, which counterintuitively enhances the lifetime of the impurity against loss. We also find a crossover from the non-Hermitian Kondo regime to the valence fluctuation regime dominated by one-body dissipation. Our results can be tested in a wide variety of setups such as quantum dots coupled to electronic leads and quantum point contacts in ultracold Fermi gases.
The equilibrium physics of quantum impurities frequently involves a universal crossover from weak to strong reservoir-impurity coupling, characterized by single-parameter scaling and an energy scale TK{T}_{K}TK​ (Kondo temperature) that breaks scale invariance. For the noninteracting resonant level model, the nonequilibrium time evolution of the Loschmidt echo after a local quantum quench was recently computed explicitly [R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett. 110, 240601 (2013)]. It shows single-parameter scaling with variable TKt{T}_{K}tTK​t. Here, we scrutinize whether similar universal dynamics can be observed in various interacting quantum impurity systems. Using density matrix and functional renormalization group approaches, we analyze the time evolution resulting from abruptly coupling two noninteracting Fermi or interacting Luttinger liquid leads via a quantum dot or a direct link. We also consider the case of a single Luttinger liquid lead suddenly coupled to a quantum dot. We investigate whether the field-theory predictions for the universal scaling as well as for the large-time behavior successfully describe the time evolution of the Loschmidt echo and the entanglement entropy of microscopic models. Our study shows that for the considered local quench protocols the above quantum impurity models fall into a class of problems for which the nonequilibrium dynamics can largely be understood based on the knowledge of the corresponding equilibrium physics.