Time-dependent numerical renormalization group method for multiple quenches: towards exact results for the long time limit of thermodynamic observables and spectral functions

We develop an alternative time-dependent numerical renormalization group (TDNRG) formalism for multiple quenches and implement it to study the response of a quantum impurity system to a general pulse. Within this approach, we reduce the contribution of the NRG approximation to numerical errors in the time evolution of observables by a formulation that avoids the use of the generalized overlap matrix elements in our previous multiple-quench TDNRG formalism [Nghiem {\em et al.,} Phys. Rev. B {\bf 89}, 075118 (2014); Phys. Rev. B {\bf 90}, 035129 (2014)]. We demonstrate that the formalism yields a smaller cumulative error in the trace of the projected density matrix as a function of time and a smaller discontinuity of local observables between quenches than in our previous approach. Moreover, by increasing the switch-on time, the time between the first and last quench of the discretized pulse, the long-time limit of observables systematically converges to its expected value in the final state, i.e., the more adiabatic the switching, the more accurately is the long-time limit recovered. The present formalism can be straightforwardly extended to infinite switch-on times. We show that this yields highly accurate results for the long-time limit of both thermodynamic observables and spectral functions, and overcomes the significant errors within the single quench formalism [Anders {\em et al.}, Phys. Rev. Lett. {\bf 95}, 196801 (2005); Nghiem {\em et al.}, Phys. Rev. Lett. {\bf 119}, 156601 (2017)]. This improvement provides a first step towards an accurate description of nonequilibrium steady states of quantum impurity systems, e.g., within the scattering states NRG approach [Anders, Phys. Rev. Lett. {\bf 101}, 066804 (2008)].Comment: 15 pages and 10 figures; Additional figures and references added; typos fixed; references fixe

Thermoelectric transport through strongly correlated quantum dots

The thermoelectric properties of strongly correlated quantum dots, described by a single level Anderson model coupled to conduction electron leads, is investigated using Wilson's numerical renormalization group method. We calculate the electronic contribution, $K_{\rm e}$, to the thermal conductance, the thermopower, $S$, and the electrical conductance, $G$, of a quantum dot as a function of both temperature, $T$, and gate voltage, ${\rm v}_g$, for strong, intermediate and weak Coulomb correlations, $U$, on the dot. For strong correlations and in the Kondo regime, we find that the thermopower exhibits two sign changes, at temperatures $T_{1}({\rm v}_g)$ and $T_{2}({\rm v}_g)$ with $T_{1}< T_{2}$. Such sign changes in $S(T)$ are particularly sensitive signatures of strong correlations and Kondo physics. The relevance of this to recent thermopower measurements of Kondo correlated quantum dots is discussed. We discuss the figure of merit, power factor and the degree of violation of the Wiedemann-Franz law in quantum dots. The extent of temperature scaling in the thermopower and thermal conductance of quantum dots in the Kondo regime is also assessed.Comment: 21 pages, 12 figures; published versio

The numerical renormalization group method for quantum impurity systems

In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG has been later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method including some guidelines of how to calculate physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean field theory.Comment: 55 pages, 27 figures, submitted to Rev. Mod. Phy

Transport Coefficients of the Anderson Model via the Numerical Renormalization Group

The transport coefficients of the Anderson model are calculated by extending Wilson's NRG method to finite temperature Green's functions. Accurate results for the frequency and temperature dependence of the single--particle spectral densities and transport time $\tau(\omega,T)$ are obtained and used to extract the temperature dependence of the transport coefficients in the strong correlation limit. The low temperature anomalies in the resistivity, $\rho(T)$, thermopower, $S(T)$, thermal conductivity $\kappa(T)$ and Hall coefficient, $R_{H}(T)$, are discussed. All quantities exhibit the expected Fermi liquid behaviour at low temperature with power law dependecies on $T/T_{K}$ in very good agreement with analytic results based on Fermi liquid theory. Scattering of conduction electrons in higher, $l>0$, angular momentum channels is also considered and an expression is derived for the corresponding transport time and used to discuss the influence of non--resonant scattering on the transport properties.Comment: 45 pages, RevTeX, 28 figures, available on reques

Real-Time-RG Analysis of the Dynamics of the Spin-Boson Model

Using a real-time renormalization group method we determine the complete dynamics of the spin-boson model with ohmic dissipation for coupling strengths $\alpha\lesssim 0.1-0.2$. We calculate the relaxation and dephasing time, the static susceptibility and correlation functions. Our results are consistent with quantum Monte Carlo simulations and the Shiba relation. We present for the first time reliable results for finite cutoff and finite bias in a regime where perturbation theory in $\alpha$ or in tunneling breaks down. Furthermore, an unambigious comparism to results from the Kondo model is achieved.Comment: 4 pages, 5 figures, 1 tabl

Out of equilibrium transport through an Anderson impurity: Probing scaling laws within the equation of motion approach

We study non-equilibrium electron transport through a quantum impurity coupled to metallic leads using the equation of motion technique at finite temperature T. Assuming that the interactions are taking place solely in the impurity and focusing in the infinite Hubbard limit, we compute the out of equilibrium density of states and the differential conductance G_2(T,V) to test several scaling laws. We find that G_2(T,V)/G_2(T,0) is a universal function of both eV/T_K and T/T_K, being T_K the Kondo temperature. The effect of an in plane magnetic field on the splitting of the zero bias anomaly in the differential conductance is also analyzed. For a Zeeman splitting \Delta, the computed differential conductance peak splitting depends only on \Delta/T_K, and for large fields approaches the value of 2\Delta . Besides the traditional two leads setup, we also consider other configurations that mimics recent experiments, namely, an impurity embedded in a mesoscopic wire and the presence of a third weakly coupled lead. In these cases, a double peak structure of the Kondo resonance is clearly obtained in the differential conductance while the amplitude of the highest peak is shown to decrease as \ln(eV/T_K). Several features of these results are in qualitative agreement with recent experimental observations reported on quantum dots.Comment: 9 pages, 7 figure

Renormalization Group Approach to Non-equilibrium Green Functions in Correlated Impurity Systems

We present a technique for calculating non-equilibrium Green functions for impurity systems with local interactions. We use an analogy to the calculation of response functions in the x-ray problem.The initial state and the final state problems, which correspond to the situations before and after the disturbance (an electric or magnetic field, for example) is suddenly switched on, are solved with the aid of Wilson's momentum shell renormalization group. The method is illustrated by calculating the non-equilibrium dynamics of the ohmic two-state problem.Comment: 7 pages, 2 figure

Inhibitor Specificity via Protein Dynamics Insights from the Design of Antibacterial Agents Targeted Against Thymidylate Synthase

AbstractStructure-based drug design of species-specific inhibitors generally exploits structural differences in proteins from different organisms. Here, we demonstrate how achieving specificity can be aided by targeting differences in the dynamics of proteins. Thymidylate synthase (TS) is a good target for anticancer agents and a potential target for antibacterial agents. Most inhibitors are folate-analogs that bind at the folate binding site and are not species specific. In contrast, α156 is not a folate-analog and is specific for bacterial TS; it has been shown crystallographically to bind in a nonconserved binding site. Docking calculations and crystal structure-based estimation of the essential dynamics of TSs from five different species show that differences in the dynamics of TSs make the active site more accessible to α156 in the prokaryotic than in the eukaryotic TSs and thereby enhance the specificity of α156

Therapeutic Education and Physical Activity to Support Self-management of Cancer-related Fatigue in Hematologic Cancer Patients: Protocol of a Feasibility Randomized Controlled Trial

Introduction: Hematologic malignancies account for nearly 8% of new cancer diagnosis in Italy. Cancer-related fatigue (CRF) is one of the most distressing symptoms reported by patients with cancer. As CRF has a multifactorial etiology, physical activity and therapeutic education may be beneficial for managing CRF, both during and after cancer treatment. However, there is a lack of evidence specific to hematologic malignancies. This paper describes the protocol of a feasibility study on Therapeutic Education and Physical Activity (TEPA) intervention to support self-management of CRF in patients with hematologic malignancies. Methods: TEPA was addressed to newly diagnosed adult individuals with hematologic malignancy able to take part in a rehabilitation programme at the AUSL-IRCCS of Reggio Emilia. The protocol was developed in 2 phases. Phase I was an observational cohort study involving a convenience sample of 10 participants with the aim to evaluate the feasibility of the assessment schedule and to register longitudinal clinical data regarding CRF (FACIT-F), psychologic distress (NCCN Distress Thermometer), QoL (EORTC QLQ-C30), physical performance (TUG and 6MWT) and habitual level of physical activity during first months after diagnosis. Phase II (underway) is a feasibility randomized controlled trial (TEPA) involving a convenience sample of 40 participants and comparing 2 parallel active interventions (Therapeutic Education versus Therapeutic Education and Physical Activity) on top of usual care. The primary aim is to estimate the feasibility of TEPA, measured by the adherence rate to the intervention. Secondary aims are: to estimate the effect size of TEPA in terms of changes in CRF, psychological distress, QoL, physical performance and habitual level of physical activity (measured as in Phase I); to collect patient satisfaction, perception of usefulness of the TEPA intervention and data on long-term adherence to an active lifestyle. Data are collected in both phases at the time of diagnosis and then at 1-, 3- (completion of intervention) and 7-month follow-up. Discussion: Data on feasibility and effect size of TEPA will be analyzed upon completion of Phase II, allowing us to design a large, adequately powered RCT to verify the effectiveness of this intervention on CRF management in patients with hematologic cancer. Trial registration: clinicaltrials.gov; Trial registration number: NCT0340307

Therapeutic education and physical activity are feasible and safe in hematologic cancer patients referred to chemotherapy: results of a randomized controlled trial

Purpose: Although over 60% of patients with hematologic cancer report distressing fatigue,&nbsp;they&nbsp;often&nbsp;do not receive recommendations on fatigue management strategies. The aim of this pilot study was to estimate the feasibility of&nbsp;therapeutic education and physical activity (TEPA)&nbsp;by measuring the patients’ adherence to this multidimensional intervention.&nbsp;The secondary aim was to&nbsp;estimate&nbsp;the impact of TEPA on clinical outcomes. Methods: Patients with hematologic cancer participated in this&nbsp;single-center, open-label,&nbsp;randomized controlled trial. The control group (CG) received two educational group sessions on fatigue and physical activity. The experimental group (EG) received the two educational sessions plus six weekly individual sessions aimed at implementing a personalized physical exercise&nbsp;program.&nbsp;Follow-ups were at 1, 3,&nbsp;and 7&nbsp;months. Results: Forty-six&nbsp;patients referred to chemotherapy were included, corresponding to 54% of recruitment rate. Adherence&nbsp;reached 90% in the EG and 68% in the CG. Most patients (65% in EG and 64% in CG) attended a minimum of 80% of the planned sessions. Overall retention rate was 87% (85% in EG and 91% in CG). No adverse events were registered. No between-group&nbsp;differences were detected in fatigue (FACIT-F), psychological distress (NCCN Distress Thermometer), QoL (EORTC QLQ-C30), or functional exercise&nbsp;capacity (TUG test and 6MWT). Adherence to an active lifestyle, measured by a semi-structured interview, increased from 56.5 to 84% in&nbsp;the EG at 7&nbsp;months (p = 0.02), whereas it decreased slightly in the CG (from 47.8 to 42.9%). Conclusion: Multidimensional rehabilitation interventions are feasible and safe in this population, and larger trials should focus on the efficacy of such approaches on clinically relevant outcomes. Trial registration: ClinicalTrials.gov Identifier: NCT03403075