arXiv subjects

Andrew K. Mitchell

Publications and source records attributed to Andrew K. Mitchell.

At least 19 recordsLinked to original sources

arXiv2026

Mapping the non-equilibrium interacting Anderson Impurity Model to an effective Gaussian theory

Quantum impurity models with strong electron correlations, such as the paradigmatic Anderson Impurity Model (AIM), are central to our understanding of a range of physical phenomena including local moment formation, Coulomb blockade and Kondo screening. They describe magnetic atoms and molecules on surfaces, quantum dot circuits, and correlated materials through dynamical mean field theory. The physics of such systems in strongly non-equilibrium conditions is particularly complex and challenging to capture, whereas Gaussian models of free fermions can be easily solved. Here we show that the time-evolving dynamics of the AIM after a quench can be described by a completely non-interacting version of the model, at the expense of coupling to additional static auxiliary degrees of freedom. Starting from the full solution of the quenched AIM using ED and DMRG, we study the properties of this mapping using numerical optimization, and uncover intriguing structure in the auxiliary system. The method allows us to understand interacting non-equilibrium dynamics through the simpler lens of an effective non-interacting system of larger dimension.

cond-mat.str-el↗

arXiv2025

Nonequilibrium steady states in multi-bath quantum collision models

Collision models provide a simple and versatile setting to capture the dynamics of open quantum systems. The standard approach to thermalisition in this setting involves an environment of independent and identically-prepared thermal qubits, interacting sequentially for a finite duration $\Delta t$ with the system. We compare this to a two-bath scenario in which collisional qubits are prepared in either their ground or excited states and the environment temperature is encoded in system-environment couplings. The system reaches the same thermal steady state for both settings, although even in this limit they describe fundamentally different physical processes, with the two-bath setup yielding a nonequilibrium state with finite heat currents. Non-Markovian dynamics arise when intra-environment interactions in either setting are introduced. Here, the system in the single-bath setup again reaches a steady state at the canonical temperature of the bath, but the nonequilibrium steady state of the two-bath setup tends to a different temperature due to the generation of strong system-environment and intra-environment correlations. The two-bath setting is particularly suited to studying quantum trajectories, which are well-defined also for the non-Markovian case. We showcase this with a trajectory analysis of the heat currents within a two-point measurement scheme. Finally, we consider how our results are impacted when the system-environment interaction leads to strict homogenisation. Our results provide insights into the dynamics and thermodynamics of thermalisation towards nonequilibrium steady states and the role of non-Markovian interactions.

quant-ph↗

arXiv2025

Roadmap on Quantum Thermodynamics

The last two decades has seen quantum thermodynamics become a well established field of research in its own right. In that time, it has demonstrated a remarkably broad applicability, ranging from providing foundational advances in the understanding of how thermodynamic principles apply at the nano-scale and in the presence of quantum coherence, to providing a guiding framework for the development of efficient quantum devices. Exquisite levels of control have allowed state-of-the-art experimental platforms to explore energetics and thermodynamics at the smallest scales which has in turn helped to drive theoretical advances. This Roadmap provides an overview of the recent developments across many of the field's sub-disciplines, assessing the key challenges and future prospects, providing a guide for its near term progress.

quant-ph↗

arXiv2025

Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model

Non-Hermitian (NH) Hamiltonians describe open quantum systems, nonequilibrium dynamics, and dissipative processes. Although a rich range of single-particle NH physics has been uncovered, many-body phenomena in strongly correlated NH systems have been far less well studied. The Kondo effect, an important paradigm for strong correlation physics, has recently been considered in the NH setting. Here we develop a NH generalization of the numerical renormalization group (NRG) and use it to solve the NH Kondo model. Our non-perturbative solution applies beyond weak coupling, and we uncover a nontrivial phase diagram. The method is showcased by application to the NH pseudogap Kondo model, which we show supports a completely novel phase with a genuine NH stable fixed point and complex eigenspectrum. Our NH-NRG code, which can be used in regimes and for models inaccessible to, e.g., perturbative scaling and Bethe ansatz, is provided open source.

cond-mat.str-el↗

arXiv2025

Metrological symmetries in singular quantum multi-parameter estimation

The theoretical foundation of quantum sensing is rooted in the Cram\'er-Rao formalism, which establishes quantitative precision bounds for a given quantum probe. In many practical scenarios, where more than one parameter is unknown, the multi-parameter Cram\'er-Rao bound (CRB) applies. Since this is a matrix inequality involving the inverse of the quantum Fisher information matrix (QFIM), the formalism breaks down when the QFIM is singular. In this paper, we examine the physical origins of such singularities, showing that they result from an over-parametrization on the metrological level. This is itself caused by emergent metrological symmetries, whereby the same set of measurement outcomes are obtained for different combinations of system parameters. Although the number of effective parameters is equal to the number of non-zero QFIM eigenvalues, the Cram\'er-Rao formalism typically does not provide information about the effective parameter encoding. Instead, we demonstrate through a series of concrete examples that Bayesian estimation can provide deep insights. In particular, the metrological symmetries appear in the Bayesian posterior distribution as lines of persistent likelihood running through the space of unknown parameters. These lines are contour lines of the effective parameters which, through suitable parameter transformations, can be estimated and follow their own effective CRBs.

quant-ph↗

arXiv2025

Quantum work statistics across a critical point: full crossover from sudden quench to the adiabatic limit

When an external parameter drives a system across a quantum phase transition at a finite rate, work is performed on the system and entropy is dissipated, due to the creation of excitations via the Kibble-Zurek mechanism. Although both the adiabatic and sudden-quench limits have been studied in detail, the quantum work statistics along the crossover connecting these limits has largely been an open question. Here we obtain exact scaling functions for the work statistics along the full crossover from adiabatic to sudden-quench limits for critical quantum impurity problems, by combining linear response theory, conformal field theory, and the numerical renormalization group. These predictions can be tested in charge-multichannel Kondo quantum dot devices, where the dissipated work corresponds to the creation of nontrivial excitations such as Majorana fermions or Fibonacci anyons.

quant-ph↗

arXiv2024

Many-body quantum interference route to the two-channel Kondo effect: Inverse design for molecular junctions and quantum dot devices

Molecular junctions -- whether actual single molecules in nanowire break junctions or artificial molecules realized in coupled quantum dot devices -- offer unique functionality due to their orbital complexity, strong electron interactions, gate control, and many-body effects from hybridization with the external electronic circuit. Inverse design involves finding candidate structures that perform a desired function optimally. Here we develop an inverse design strategy for generalized quantum impurity models describing molecular junctions, and as an example, use it to demonstrate that many-body quantum interference can be leveraged to realize the two-channel Kondo critical point in simple 4- or 5-site molecular moieties. We show that remarkably high Kondo temperatures can be achieved, meaning that entropy and transport signatures should be experimentally accessible.

cond-mat.mes-hall↗

arXiv2024

Multiparameter critical quantum metrology with impurity probes

Quantum systems can be used as probes in the context of metrology for enhanced parameter estimation. In particular, the delicacy of critical systems to perturbations can make them ideal sensors. Arguably the simplest realistic probe system is a spin-1/2 impurity, which can be manipulated and measured in-situ when embedded in a fermionic environment. Although entanglement between a single impurity probe and its environment produces nontrivial many-body effects, criticality cannot be leveraged for sensing. Here we introduce instead the two-impurity Kondo (2IK) model as a novel paradigm for critical quantum metrology, and examine the multiparameter estimation scenario at finite temperature. We explore the full metrological phase diagram numerically and obtain exact analytic results near criticality. Enhanced sensitivity to the inter-impurity coupling driving a second-order phase transition is evidenced by diverging quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR). However, with uncertainty in both coupling strength and temperature, the multiparameter QFI matrix becomes singular -- even though the parameters to be estimated are independent -- resulting in vanishing QSNRs. We demonstrate that by applying a known control field, the singularity can be removed and measurement sensitivity restored. For general systems, we show that the degradation in the QSNR due to uncertainties in another parameter is controlled by the degree of correlation between the unknown parameters.

quant-ph↗

arXiv2024

Quantum Sensing with Nanoelectronics: Fisher Information for an Applied Perturbation

Quantum systems used for metrology can offer enhanced precision over their classical counterparts. The design of quantum sensors can be optimized by maximizing the quantum Fisher information (QFI), which characterizes the precision of parameter estimation for an ideal measurement. Here we consider the response of a quantum system as a means to estimate the strength of a weak external perturbation. General expressions for the QFI in the nonequilibrium steady-state are derived, which hold for arbitrary interacting many-body systems at finite or zero temperature, and can be related to susceptibilities or linear-response transport coefficients. For quantum dot nanoelectronics devices, we show that electron interactions can lead to *exponential* scaling of the QFI with system size, highlighting that quantum resources can be utilized in the full Fock space. The precision estimation of voltages and fields can also be achieved by practical measurements. In particular, we show that current-based metrology in quantum circuits can leverage many-body effects for enhanced sensing.

quant-ph↗

arXiv2024

Nanoscale single-electron box with a floating lead for quantum sensing: modelling and device characterization

We present an in-depth analysis of a single-electron box (SEB) biased through a floating node technique that is common in charge-coupled devices (CCDs). The device is analyzed and characterized in the context of single-electron charge-sensing techniques for integrated silicon quantum dots (QD). The unique aspect of our SEB design is the incorporation of a metallic floating node, strategically employed for sensing and precise injection of electrons into an electrostatically formed QD. To analyse the SEB, we propose an extended multi-orbital Anderson impurity model (MOAIM), adapted to our nanoscale SEB system, that is used to predict theoretically the behaviour of the SEB in the context of a charge-sensing application. The validation of the model and the sensing technique has been carried out on a QD fabricated in a fully depleted silicon on insulator (FDSOI) process on a 22-nm technological node. We demonstrate the MOAIM's efficacy in predicting the observed electronic behavior and elucidating the complex electron dynamics and correlations in the SEB. The results of our study reinforce the versatility and precision of the model in the realm of nanoelectronics and highlight the practical utility of the metallic floating node as a mechanism for charge injection and detection in integrated QDs. Finally, we identify the limitations of our model in capturing higher-order effects observed in our measurements and propose future outlooks to reconcile some of these discrepancies.

cond-mat.mes-hall↗

arXiv2024

Unsupervised Learning of Effective Quantum Impurity Models

Generalized quantum impurity models -- which feature a few localized and strongly-correlated degrees of freedom coupled to itinerant conduction electrons -- describe diverse physical systems, from magnetic moments in metals to nanoelectronics quantum devices such as quantum dots or single-molecule transistors. Correlated materials can also be understood as self-consistent impurity models through dynamical mean field theory. Accurate simulation of such models is challenging, especially at low temperatures, due to many-body effects from electronic interactions, resulting in strong renormalization. In particular, the interplay between local impurity complexity and Kondo physics is highly nontrivial. A common approach, which we further develop in this work, is to consider instead a simpler effective impurity model that still captures the low-energy physics of interest. The mapping from bare to effective model is typically done perturbatively, but even this can be difficult for complex systems, and the resulting effective model parameters can anyway be quite inaccurate. Here we develop a non-perturbative, unsupervised machine learning approach to systematically obtain low-energy effective impurity-type models, based on the renormalization group framework. The method is shown to be general and flexible, as well as accurate and systematically improvable. We benchmark the method against exact results for the Anderson impurity model, and provide an outlook for more complex models beyond the reach of existing methods.

cond-mat.str-el↗

arXiv2023

Kondo effect in twisted bilayer graphene

The emergence of flat bands in twisted bilayer graphene at the magic angle can be understood in terms of a vanishing Fermi velocity of the Dirac cone. This is associated with van Hove singularities approaching the Fermi energy and becoming higher-order. In the density of states this is reflected by flanking logarithmic van Hove divergences pinching off the central Dirac cone in energy space. The low-energy pseudogap of the Dirac cone away from the magic angle is replaced by a power-law divergence due to the higher-order van Hove singularity at the magic angle. This plays an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. Here we investigate one such correlation effect -- the Kondo effect due to a magnetic impurity embedded in twisted bilayer graphene. We use the Bistritzer-MacDonald model to extract the low-energy density of states of the material as a function of twist angle, and study the resulting quantum impurity physics using perturbative and numerical renormalization group methods. Although at zero temperature the impurity is only Kondo screened precisely at the magic angle, we find highly nontrivial behavior at finite temperatures relevant to experiment, due to the complex interplay between Dirac, van Hove, and Kondo physics.

cond-mat.str-el↗

arXiv2023

$\mathbb{Z}_3$ parafermion in the double charge-Kondo model

Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a $\mathbb{Z}_3$ parafermion emerges at the critical point, characterized by a fractional $\tfrac{1}{2}\ln(3)$ residual entropy, and scattering fractional charges $e/3$. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results.

cond-mat.mes-hall↗

arXiv2023

Thermometry of Strongly Correlated Fermionic Quantum Systems using Impurity Probes

We study quantum impurity models as a platform for quantum thermometry. A single quantum spin-1/2 impurity is coupled to an explicit, structured, fermionic thermal environment which we refer to as the environment or bath. We critically assess the thermometric capabilities of the impurity as a probe, when its coupling to the environment is of Ising or Kondo exchange type. In the Ising case, we find sensitivity equivalent to that of an idealized two-level system, with peak thermometric performance obtained at a temperature that scales linearly in the applied control field, independent of the coupling strength and environment spectral features. By contrast, a richer thermometric response can be realized for Kondo impurities, since strong probe-environment entanglement can then develop. At low temperatures, we uncover a regime with a universal thermometric response that is independent of microscopic details, controlled only by the low-energy spectral features of the environment. The many-body entanglement that develops in this regime means that low-temperature thermometry with a weakly applied control field is inherently less sensitive, while optimal sensitivity is recovered by suppressing the entanglement with stronger fields.

quant-ph↗

arXiv2022

Two-channel charge-Kondo physics in graphene quantum dots

Nanoelectronic quantum dot devices exploiting the charge-Kondo paradigm have been established as versatile and accurate analog quantum simulators of fundamental quantum impurity models. In particular, hybrid metal-semiconductor dots connected to two metallic leads realize the two-channel Kondo (2CK) model, in which Kondo screening of the dot charge pseudospin is frustrated. Here, we consider theoretically a two-channel charge-Kondo device made instead from graphene components, realizing a pseudogapped version of the 2CK model. We solve the model using Wilson's Numerical Renormalization Group method, and uncover a rich phase diagram as a function of dot-lead coupling strength, channel asymmetry, and potential scattering. The complex physics of this system is explored through its thermodynamic properties, scattering T-matrix, and experimentally measurable conductance. We find that the strong coupling pseudogap Kondo phase persists in the channel-asymmetric two-channel context, while in the channel-symmetric case frustration results in a novel quantum phase transition. Remarkably, despite the vanishing density of states in the graphene leads at low energies, we find a finite linear conductance at zero temperature at the frustrated critical point, which is of non-Fermi liquid type. Our results suggest that the graphene charge-Kondo platform offers a unique possibility to access multichannel pseudogap Kondo physics.

cond-mat.str-el↗

arXiv2022

Linear response quantum transport through interacting multi-orbital nanostructures

Nanoelectronics devices, such as quantum dot systems or single-molecule transistors, consist of a quantum nanostructure coupled to a macroscopic external electronic circuit. Thermoelectric transport between source and drain leads is controlled by the quantum dynamics of the lead-coupled nanostructure, through which a current must pass. Strong electron interactions due to quantum confinement on the nanostructure produce nontrivial conductance signatures such as Coulomb blockade and Kondo effects, which become especially pronounced at low temperatures. In this work we first provide a modern review of standard quantum transport techniques, focusing on the linear response regime, and highlight the strengths and limitations of each. In the second part, we develop an improved numerical scheme for calculation of the ac linear electrical conductance through generic interacting nanostructures, based on the numerical renormalization group (NRG) method, and explicitly demonstrate its utility in terms of accuracy and efficiency. In the third part we derive low-energy effective models valid in various commonly-encountered situations, and from them we obtain simple analytical expressions for the low-temperature conductance. This indirect route via effective models, although approximate, allows certain limitations of conventional methodologies to be overcome, and provides physical insights into transport mechanisms. Finally, we apply and compare the various techniques, taking the two-terminal triple quantum dot and the serial multi-level double dot devices as nontrivial benchmark systems.

cond-mat.str-el↗

arXiv2022

Fractional entropy of multichannel Kondo systems from conductance-charge relations

Fractional entropy is a signature of nonlocal degrees of freedom, such as Majorana zero modes or more exotic non-Abelian anyons. Although direct experimental measurements remain challenging, Maxwell relations provide an indirect route to the entropy through charge measurements. Here we consider multichannel charge-Kondo systems, which are predicted to host exotic quasiparticles due to a frustration of Kondo screening at low temperatures. In the absence of experimental data for the charge occupation, we derive relations connecting the latter to the conductance, for which experimental results have recently been obtained. Our analysis indicates that Majorana and Fibonacci anyon quasiparticles are well-developed in existing two- and three-channel charge-Kondo devices, and that their characteristic $k_{\rm{B}}\log\sqrt{2}$ and $k_{\rm{B}}\log\frac{1+\sqrt{5}}{2}$ entropies are experimentally measurable.

cond-mat.mes-hall↗

arXiv2022

Automatic Differentiable Numerical Renormalization Group

Machine learning techniques have recently gained prominence in physics, yielding a host of new results and insights. One key concept is that of backpropagation, which computes the exact gradient of any output of a program with respect to any input. This is achieved efficiently within the differentiable programming paradigm, which utilizes automatic differentiation (AD) of each step of a computer program and the chain rule. A classic application is in training neural networks. Here, we apply this methodology instead to the numerical renormalization group (NRG), a powerful technique in computational quantum many-body physics. We demonstrate how derivatives of NRG outputs with respect to Hamiltonian parameters can be accurately and efficiently obtained. Physical properties can be calculated using this differentiable NRG scheme--for example, thermodynamic observables from derivatives of the free energy. Susceptibilities can be computed by adding source terms to the Hamiltonian, but still evaluated with AD at precisely zero field. As an outlook, we briefly discuss the derivatives of dynamical quantities and a possible route to the vertex.

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