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Volker Meden

Publications and source records attributed to Volker Meden.

At least 19 recordsLinked to original sources
arXiv2026

Quantum critical properties of non-Hermitian XY models with magnetic field

The characterization of the quantum critical properties of genuine non-Hermitian many-body systems remains ambiguous as neither the state considered nor the definition of expectation values is unique. In this work, we investigate the quantum critical properties of two models of non-Hermitian XY spin chains with magnetic field. Using exact solutions, we systematically investigate the parameter dependence of the energy, the magnetization as well as the long-distance asymptotic behavior of static correlation functions. We compute expectation values within the standard formalism of quantum mechanics as well as within biorthogonal quantum mechanics and take two different states which one might reasonably consider to be the analog of the ground state of a Hermitian model. The critical properties, including such fundamental characteristics as the phase diagram, depend on both the formalism used as well as the state considered. We provide arguments in favor of the use of standard quantum mechanics. Which state to be taken in computations, depends on the (hypothetical) experimental preparation of the system.

quant-ph↗
arXiv2024

Simulating electron-vibron energy transfer with quantum dots and resonators

Gateable semiconductor quantum dots (QDs) provide a versatile platform for analog quantum simulations of electronic many-body systems. In particular, QD arrays offer a natural representation of the interacting $\pi$-electron system of small hydrocarbons. Here we investigate the prospects for extending QD simulators to encompass also the nuclear degrees of freedom. We represent the molecular vibrational modes by single-mode microwave resonators coupled capacitively to the QDs and study the gate-tunable energy transfer from a voltage-biased triple quantum dot (TQD) system to a single damped resonator mode. We determine the QD population inversions, the corresponding charge and energy currents as well as the resonator photon number, using Lindblad master equations and lowest-order perturbation theory within Keldysh Green function formalism. Along the way, we discuss the merits and shortcomings of the two methods.A central result is the interrelation of a pronounced minimum in the charge current with a maximum in energy transfer, arising from a gate-tunable interference effect in the molecular orbitals of the TQD electron system.

cond-mat.mes-hall↗
arXiv2022

Functional renormalization group for non-Hermitian and $\mathcal{PT}$-symmetric systems

We generalize the vertex expansion approach of the functional renormalization group to non-Hermitian systems. As certain anomalous expectation values might not vanish, additional terms as compared to the Hermitian case can appear in the flow equations. We investigate the merits and shortcomings of the vertex expansion for non-Hermitian systems by considering an exactly solvable $\mathcal{PT}$-symmetric non-linear toy-model and reveal, that in this model, the fidelity of the vertex expansion in a perturbatively motivated truncation schema is comparable with that of the Hermitian case. The vertex expansion appears to be a viable method for studying correlation effects in non-Hermitian systems.

cond-mat.str-el↗
arXiv2022

Conductance of correlated many-fermion systems from charge fluctuations

We put forward a relation between the static charge fluctuations and the conductance of correlated many-fermion systems at zero temperature, avoiding the use of time-dependent fluctuations as in the fluctuation-dissipation theorem. Static charge fluctuations can efficiently be computed for low-dimensional systems using tensor network approaches, while the conductance is often significantly more difficult to obtain, requiring a challenging low-frequency linear response computation or an explicit time evolution. We put this relation to the test for quantum dot and quantum point contact setups, where in limiting cases exact results are known. Our study includes systems in which the one-dimensional reservoirs are interacting.

cond-mat.str-el↗
arXiv2022

Quantum dot coupled to topological insulators: The role of edge states

We investigate a system consisting of one or two topological-insulator leads which are tunnel coupled to a single dot level. The leads are described by the one-dimensional Su-Schrieffer-Heeger model. We show that (topological) edge states cause characteristic features in the dot spectral function, the dot occupation, and the finite-bias current across the dot. As the kinetic energy is quenched in the dot region, local two-particle interactions are of particular relevance there. This motivates us to test whether the aforementioned edge-state features are robust against such interactions; we report here that they are either robust or even enhanced. We conclude that the characteristic features can be used to determine if the leads are in their topologically non-trivial or trivial phase.

cond-mat.mes-hall↗
arXiv2020

Friedel oscillations of one-dimensional correlated fermions from perturbation theory and density functional theory

We study the asymptotic decay of the Friedel density oscillations induced by an open boundary in a one-dimensional chain of lattice fermions with a short-range two-particle interaction. From Tomonaga-Luttinger liquid theory it is known that the decay follows a power law, with an interaction dependent exponent, which, for repulsive interactions, is larger than the noninteracting value $-1$. We first investigate if this behavior can be captured by many-body perturbation theory for either the Green function or the self-energy in lowest order in the two-particle interaction. The analytic results of the former show a logarithmic divergence indicative of the power law. One might hope that the resummation of higher order terms inherent to the Dyson equation then leads to a power law in the perturbation theory for the self-energy. However, the numerical results do not support this. Next we use density functional theory within the local-density approximation and an exchange-correlation functional derived from the exact Bethe ansatz solution of the translational invariant model. While the numerical results are consistent with power-law scaling if systems of $10^4$ or more lattice sites are considered, the extracted exponent is very close to the noninteracting value even for sizeable interactions.

cond-mat.str-el↗
arXiv2019

RG transport theory for open quantum systems: Charge fluctuations in multilevel quantum dots in and out of equilibrium

We present the real-time renormalization group (RTRG) method as a method to describe the stationary state current through generic multi-level quantum dots with a complex setup in nonequilibrium. The employed approach consists of a very rudiment approximation for the RG equations which neglects all vertex corrections while it provides a means to compute the effective dot Liouvillian self-consistently. Being based on a weak-coupling expansion in the tunneling between dot and reservoirs, the RTRG approach turns out to reliably describe charge fluctuations in and out of equilibrium for arbitrary coupling strength, even at zero temperature. We confirm this in the linear response regime with a benchmark against highly-accurate numerically renormalization group data in the exemplary case of three-level quantum dots. For small to intermediate bias voltages and weak Coulomb interactions, we find an excellent agreement between RTRG and functional renormalization group data, which can be expected to be accurate in this regime. As a consequence, we advertise the presented RTRG approach as an efficient and versatile tool to describe charge fluctuations theoretically in quantum dot systems.

cond-mat.str-el↗
arXiv2018

Detecting phases in one-dimensional many-fermion systems with the functional renormalization group

The functional renormalization group (FRG) has been used widely to investigate phase diagrams, in particular the one of the two-dimensional Hubbard model. So far, the study of one-dimensional models has not attracted as much attention. We use the FRG to investigate the phases of a one-dimensional spinless tight-binding chain with nearest and next-nearest neighbor interactions at half filling. The phase diagram of this model has already been established with other methods, and phase transitions from a metallic phase to ordered phases take place at intermediate to strong interactions. The model is thus well suited to analyze the potential and the limitations of the FRG in this regime of interactions. We employ flow equations that are exact up to second order in the interaction, which implies that we take into account the frequency dependence of the two-particle vertex as well as the feedback of the dynamic self-energy. For intermediate nearest neighbor interactions, our scheme captures the phase transition from a metallic phase to a charge density wave with alternating occupation. The critical interaction, at which this transition occurs, is underestimated due to our approximations. Similarly, for intermediate next-nearest neighbor interactions, we observe a transition to a charge density wave with occupation pattern ..00110011... We show that taking into account a feedback of the two-particle vertex in the flow equation is essential for the detection of those phases.

cond-mat.str-el↗
arXiv2016

Functional renormalization group in Floquet space

We present an extension of the functional renormalization group to Floquet space, which enables us to treat the long time behavior of interacting time periodically driven quantum dots. It is one of its strength that the method is neither bound to small driving amplitudes nor to small driving frequencies, i.e. very general time periodic signals can be considered. It is applied to the interacting resonant level model, a prototype model of a spinless, fermionic quantum dot. The renormalization in several setups with different combinations of time periodic parameters is studied, where the numerical results are complemented by analytic expressions for the renormalization in the limit of small driving amplitude. We show how the driving frequency acts as an infrared cutoff of the underlying renormalization group flow which manifests in novel power laws. We utilize the tunability of the effective reservoir distribution function in a periodically driven onsite energy setup to show how its shape is directly reflected in the renormalization group flow. This allows to flexibly tune the power-law renormalization generically encountered in quantum dot structures. Finally, an in-phase quantum pump as well as a single parameter pump are investigated in the whole regime of driving frequency, demonstrating that the new power law in the driving frequency is reflected in the mean current of the latter.

cond-mat.str-el↗
arXiv2016

Magneto-electric spectroscopy of Andreev bound states in Josephson quantum dots

We theoretically investigate the behavior of Andreev levels in a single-orbital interacting quantum dot in contact to superconducting leads, focusing on the effect of electrostatic gating and applied magnetic field, as relevant for recent experimental spectroscopic studies. In order to account reliably for spin-polarization effects in presence of correlations, we extend here two simple and complementary approaches that are tailored to capture effective Andreev levels: the static functional renormalization group (fRG) and the self-consistent Andreev bound states (SCABS) theory. We provide benchmarks against the exact large-gap solution as well as NRG calculations and find good quantitative agreement in the range of validity. The large flexibility of the implemented approaches then allows us to analyze a sizeable parameter space, allowing to get a deeper physical understanding into the Zeeman field, electrostatic gate, and flux dependence of Andreev levels in interacting nanostructures.

cond-mat.str-el↗
arXiv2016

Renormalization group flow of the Luttinger-Ward functional: conserving approximations and application to the Anderson impurity model

We study the renormalization group flow of the Luttinger-Ward functional and of its two-particle irreducible vertex functions, given a cut-off in the two-particle interaction. We derive a conserving approximation to the flow and relate it to the fluctuation exchange approximation as well as to non-conserving approximations introduced in an earlier publication ctuation exchange approximation as well as to nonconserving approximations introducen [J. F. Rentrop, S. G. Jakobs, and V. Meden, J. Phys. A: Math. Theor. 48, 145002 (2015)]. We apply the different approximate flow equations to the single impurity Anderson model in thermal equilibrium at vanishing temperature. Numerical results for the effective mass, the spin susceptibility, the charge susceptibility, and the linear conductance reflect the similarity of the methods to the fluctuation exchange approximation. We find the majority of the approximations to deviate stronger from the exact results than one-particle irreducible functional renormalization group schemes. However, we identify a simple static two-particle irreducible flow scheme which performs remarkably well and produces an exponential Kondo-like scale in the renormalized level position.

cond-mat.str-el↗
arXiv2015

Two-particle irreducible functional renormalization group schemes---a comparative study

We derive functional renormalization group schemes for Fermi systems which are based on the two-particle irreducible approach to the quantum many-body problem. In a first step, the cutoff is introduced in the non-interacting propagator as it is commonly done in functional renormalization group based on one-particle irreducible vertex functions. The most natural truncation of the resulting infinite hierarchy of flow equations is shown to be fully equivalent to self-consistent perturbation theory. An earlier suggested alternative truncation strategy is considered as well. In a second step, the cutoff is introduced in the two-particle interaction. Again two truncation procedures are investigated, one of which was derived before. In the latter, the mean-field solution of the many-body problem is considered as the starting point of the renormalization group flow. We compare the performance and the required numerical resources for solving the coupled flow equations for all the approximate schemes by applying them to the problem of the quantum anharmonic oscillator. In a functional integral representation, this model has a formal similarity to the quantum many-body problem. The perspectives for applying the derived two-particle irreducible functional renormalization group approaches to zero- and one-dimensional systems of correlated fermions are discussed.

cond-mat.str-el↗
arXiv2014

Non-equilibrium transport through a Josephson quantum dot

We study the electronic current through a quantum dot coupled to two superconducting leads which is driven by either a voltage $V$ or temperature $ΔT$ bias. Finite biases beyond the linear response regime are considered. The local two-particle interaction $U$ on the dot is treated using an approximation scheme within the functional renormalization group approach set up in Keldysh-Nambu-space with $U$ being the small parameter. For $V>0$ we compare our renormalization group enhanced results for the dc-component of the current to earlier weak coupling approaches such as the Hartree-Fock approximation and second order perturbation theory in $U$. We show that in parameter regimes in which finite bias driven multiple Andreev reflections prevail small $|U|$ approaches become unreliable for interactions of appreciable strength. In the complementary regime the convergence of the current with respect to numerical parameters becomes an issue - but can eventually be achieved - and interaction effects turn out to be smaller then expected based on earlier results. For $ΔT>0$ we find a surprising increase of the current as a function of the superconducting phase difference in the regime which at $T=0$ becomes the $π$ (doublet) phase.

cond-mat.str-el↗
arXiv2013

The quench dynamics of a dissipative quantum system: a renormalization group study

We study dissipation in a small quantum system coupled to an environment held in thermodynamic equilibrium. The relaxation dynamics of a system subject to an abrupt quench in the parameters of the underlying Hamiltonian is investigated using two complementary renormalization group approaches. The methods are applied to the Ohmic spin-boson model close to the coherent-to-incoherent transition. In particular, the role of non-Markovian memory for the relaxation before and after the quench of the spin-boson coupling and the Zeeman splitting of the up and down spin is investigated.

cond-mat.mes-hall↗
arXiv2012

Functional renormalization group approach to correlated fermion systems

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems, (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals, (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and non-equilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. We present a self-contained derivation of the exact flow equations and describe frequently used truncation schemes. Reviewing selected applications we then show how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.

cond-mat.str-el↗
arXiv2012

Understanding the Josephson current through a Kondo-correlated quantum dot

We study the Josephson current 0-$π$ transition of a quantum dot tuned to the Kondo regime. The physics can be quantitatively captured by the numerically exact continuous time quantum Monte Carlo method applied to the single-impurity Anderson model with BCS superconducting leads. For a comparison to an experiment the tunnel couplings are determined by fitting the normal-state linear conductance. Excellent agreement for the dependence of the critical Josephson current on the level energy is achieved. For increased tunnel couplings the Kondo scale becomes comparable to the superconducting gap and the regime of the strongest competition between superconductivity and Kondo correlations is reached; we predict the gate voltage dependence of the critical current in this regime.

cond-mat.str-el↗
arXiv2012

Quench dynamics of correlated quantum dots

We study the relaxation dynamics of a quantum dot with local Coulomb correlations coupled to two noninteracting leads which are held in grandcanonical equilibrium. Only charge degrees of freedom are considered and the dot is described by a model which in the scaling limit becomes equivalent to the interacting resonant level model. The time evolution of the current and dot occupancy resulting out of changes of the dot-lead coupling, the dots onsite energy, or the charging energy are studied. Abrupt and smooth parameter changes as well as setups with and without driving bias voltage are considered. For biased dots we investigate the often studied response after turning on the dot-lead coupling but also the experimentally more relevant case in which the voltage is turned on. We identify and explain a variety of interesting many-body effects and clarify the role of initial correlations.

cond-mat.str-el↗