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arXiv:2412.00801 · Physical review. B./Physical review. B

Realizing the interacting resonant level model using a quantum dot detector

Zhanyu Ma, Matan Lotem, Yigal Meir, Eran Sela

Published Mar 6, 2025• 3 citations
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Abstract

The interacting resonant level model (IRLM) is the simplest quantum impurity model to display strongly correlated effects in mesoscopic systems, which triggered its extensive theoretical study. However, to date, there have not been any realizations of the model with controllable interaction parameter, and thus the detailed predictions could not be confirmed. Here we use a recently developed approach to Anderson orthogonality catastrophe physics, using a charge detector coupled to a quantum dot (QD) system, to devise a simple experimental system which could display IRLM behavior and detail its predictions. At the same time, the mapping to IRLM allows us to determine the interaction parameter of the charge detector using simple experimental probes.

DOI
10.1103/physrevb.111.115117

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The interacting resonant level model (IRLM) is the simplest quantum impurity model to display strongly correlated effects in mesoscopic systems, which triggered its extensive theoretical study. However, to date, there have not been any realizations of the model with controllable interaction parameter, and thus the detailed predictions could not be confirmed. Here we use a recently developed approach to Anderson orthogonality catastrophe physics, using a charge detector coupled to a quantum dot (QD) system, to devise a simple experimental system which could display IRLM behavior and detail its predictions. At the same time, the mapping to IRLM allows us to determine the interaction parameter of the charge detector using simple experimental probes.
We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of the single-particle wave functions constituting the Fermi sea have to adjust in response to the sudden change in the local parameters of the Hamiltonian, causing the initial and final ground states to be orthogonal. This so-called Anderson orthogonality catastrophe also influences dynamical properties, such as spectral functions. Their low-frequency behavior shows nontrivial power laws, with exponents that can be understood using a generalization of simple arguments introduced by Hopfield and others for the x-ray edge singularity problem. The goal of this work is to formulate these generalized rules as well as to numerically illustrate them for quantum quenches in impurity models involving local interactions. As a simple yet instructive example, we use the interacting resonant level model as testing ground for our generalized Hopfield rule. We then analyze a model exhibiting population switching between two dot levels as a function of gate voltage, probed by a local Coulomb interaction with an additional lead serving as charge sensor. We confirm a recent prediction that charge sensing can induce a quantum phase transition for this system, causing the population switch to become abrupt. We elucidate the role of Anderson orthogonality for this effect by explicitly calculating the relevant orthogonality exponents.
In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the Interacting Resonant Level Model (IRLM), at low energy (i.e. in the strong coupling regime). We use integrability results for the Kondo model to describe the infrared fixed point, conformal field theory techniques initially developed by Cardy and Calabrese and a quantization scheme that allows one to compute exactly Renyi entropies at arbitrary order in 1/TB in principle, even when the system size or the temperature is finite. We show that those universal quantities at arbitrary interaction parameter in the strong coupling regime are very well approximated by the same quantities in the free fermion system in the case of attractive Coulomb interaction, whereas a strong dependence on the interaction appears in the case of repulsive interaction.
Measurement perturbs a quantum system by coupling it to external degrees of freedom, but detector backaction depends on the physical mechanism of measurement itself. In solid-state devices, detectors driven far from equilibrium to enable faster measurements produce backaction that can often be understood as classical noise. However, a strong measurement can also induce backaction from quantum many-body correlations in the detector that are intrinsic to the measurement, even without shot noise. Here, we probe this near-equilibrium backaction through the effect of a quantum-dot charge sensor on tunnelling between a second quantum dot and its reservoirs. The measurement realizes the Anderson Orthogonality Catastrophe (AOC): electrons in the detector leads reorganize in response to an abrupt change in local scattering potential, suppressing resonant tunnelling while enabling inelastic processes that exchange energy with the detector. Changing the detector energy level tunes the AOC backaction from negligible to dominant in the tunnelling dynamics. More broadly, these results establish detector-induced many-body correlations as a controllable influence on quantum dynamics.
We study the Anderson impurity problem in a mesoscopic setting, namely the ``Anderson box,'' in which the impurity is coupled to finite reservoir having a discrete spectrum and large sample-to-sample mesoscopic fluctuations. Note that both the weakly coupled and strong coupling Anderson impurity problems are characterized by a Fermi-liquid theory with weakly interacting quasiparticles. We study how the statistical fluctuations in these two problems are connected, using random matrix theory and the slave boson mean-field approximation (SBMFA). First, for a resonant level model such as results from the SBMFA, we find the joint distribution of energy levels with and without the resonant level present. Second, if only energy levels within the Kondo resonance are considered, the distributions of perturbed levels collapse to universal forms for both orthogonal and unitary ensembles for all values of the coupling. These universal curves are described well by a simple Wigner-surmise-type toy model. Third, we study the fluctuations of the mean-field parameters in the SBMFA, finding that they are small. Finally, the change in the intensity of an eigenfunction at an arbitrary point is studied, such as is relevant in conductance measurements. We find that the introduction of the strongly coupled impurity considerably changes the wave function but that a substantial correlation remains.
Using time-dependent density matrix renormalization group calculations we study the transport properties ($I\ensuremath{-}V$ curves and shot noise) of the interacting resonant level model (IRLM) in a large range of the interaction parameter UUU, in the scaling limit. We find that these properties can be described remarkably well by those of the boundary sine-Gordon model (BSG), which are known analytically [Fendley et al., Phys. Rev. B 52, 8934 (1995).]. We argue that the two models are nevertheless in different universality classes out-of-equilibrium: this requires a delicate discussion of their infrared (IR) properties (i.e., at low bias), where we prove in particular that the effective tunneling charge is eee in the infrared regime of the IRLM (except at the self-dual point where it jumps to 2e2e2e), while it is known to be a continuously varying function of UUU in the BSG. This behavior is confirmed by careful analysis of the numerical data in the IR. The remarkable agreement of the transport properties, especially in the crossover region, remains however unexplained.
Luttinger-liquid behavior of one-dimensional correlated electron systems is characterized by power-law scaling of a variety of physical observables with exponents determined by a single interaction dependent parameter KKK. We suggest a setup to study Luttinger-liquid behavior in quantum wires which allows us to determine KKK from two independent measurements: transport through a quantum dot embedded in the wire and the charge on the dot. Consistency of the two KKK's for a single probe would provide strong experimental evidence for the Luttinger-liquid paradigm.