Research using NRG Ljubljana

NRG Ljubljana is used in research on quantum dots, Kondo systems, superconducting impurities, molecular magnets, dynamical mean-field theory (DMFT), and correlated materials.

The papers below are a representative, non-exhaustive selection of published applications. Each paper explicitly identifies NRG Ljubljana, its project website, or its archived software record in connection with the calculations. The selection includes work from independent research groups as well as application papers co-authored by project maintainers; core software papers are not counted as applications.

If you publish work using NRG Ljubljana, please submit a pull request or open an issue so that it can be added here.

Quantum dots, Kondo systems, and nanostructures

  • Kondo effect in a two-dimensional electron gas in the persistent spin helix regime. T. O. Puel, M. A. Manya, G. S. Diniz, E. Vernek, and G. B. Martins. Physical Review B (2025). doi:10.1103/cm2n-y4c3. NRG Ljubljana was used to calculate impurity thermodynamics and Kondo scales in the presence of balanced Rashba and Dresselhaus spin-orbit coupling.

  • Suppressed Kondo screening in two-dimensional altermagnets. G. S. Diniz and E. Vernek. Physical Review B (2024). doi:10.1103/PhysRevB.109.155127. NRG Ljubljana was used to solve an Anderson impurity coupled to altermagnetic hosts and determine how their spin-dependent density of states suppresses Kondo screening.

  • Quantum impurity with 2/3 local moment in one-dimensional quantum wires: A numerical renormalization group study. P. A. Almeida, M. A. Manya, M. S. Figueira, S. E. Ulloa, E. V. Anda, and G. B. Martins. Physical Review B (2024). doi:10.1103/PhysRevB.109.045112. NRG Ljubljana was used to compute spectra, thermodynamics, and energy flows revealing the fractional local moment produced by a band-edge bound state.

  • Kondo cloud in a one-dimensional nanowire. Joseph Kleinhenz, Igor Krivenko, Guy Cohen, and Emanuel Gull. Physical Review B (2022). doi:10.1103/PhysRevB.105.085126. TRIQS wrappers around NRG Ljubljana supplied impurity Green's functions and thermodynamic scales for the analysis of the spatial Kondo cloud.

  • Kondo screening regimes in multi-Dirac and Weyl systems. G. T. D. Pedrosa, Joelson F. Silva, and E. Vernek. Physical Review B (2021). doi:10.1103/PhysRevB.103.045137. NRG Ljubljana was used to map impurity screening regimes from spectral and thermodynamic properties of multi-Dirac and Weyl hosts.

Superconducting impurities and Yu-Shiba-Rusinov states

  • Tracking a spin-polarized superconducting bound state across a quantum phase transition. Sujoy Karan, Haonan Huang, Alexander Ivanovic, Ciprian Padurariu, Björn Kubala, Klaus Kern, Joachim Ankerhold, and Christian R. Ast. Nature Communications (2024). doi:10.1038/s41467-024-44708-2. NRG Ljubljana was used to model the tunneling spectra and spin polarization of a bound state as it crossed the singlet-doublet transition.

  • Universal scaling of tunable Yu-Shiba-Rusinov states across the quantum phase transition. Haonan Huang, Sujoy Karan, Ciprian Padurariu, Björn Kubala, Juan Carlos Cuevas, Joachim Ankerhold, Klaus Kern, and Christian R. Ast. Communications Physics (2023). doi:10.1038/s42005-023-01332-8. NRG Ljubljana was used to calculate Yu-Shiba-Rusinov excitation energies and spectral weights and demonstrate their universal scaling.

  • Spin-orbital Yu-Shiba-Rusinov states in single Kondo molecular magnet. Hui-Nan Xia, Emi Minamitani, Rok Žitko, Zhen-Yu Liu, Xin Liao, Min Cai, Zi-Heng Ling, Wen-Hao Zhang, Svetlana Klyatskaya, Mario Ruben, and Ying-Shuang Fu. Nature Communications (2022). doi:10.1038/s41467-022-34187-8. NRG Ljubljana was used to solve a multiorbital impurity model and assign two pairs of subgap states to distinct spin and orbital degrees of freedom.

  • Singlet-Doublet Transitions of a Quantum Dot Josephson Junction Detected in a Transmon Circuit. Arno Bargerbos, Marta Pita-Vidal, Rok Žitko, Jesús Ávila, Lukas J. Splitthoff, Lukas Grünhaupt, Jaap J. Wesdorp, Christian K. Andersen, Yu Liu, Leo P. Kouwenhoven, Ramón Aguado, Angela Kou, and Bernard van Heck. PRX Quantum (2022). doi:10.1103/PRXQuantum.3.030311. NRG Ljubljana was used to calculate the phase-dependent singlet-doublet spectrum measured through the transmon circuit.

  • Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads. Peter Zalom, Vladislav Pokorný, and Tomáš Novotný. Physical Review B (2021). doi:10.1103/PhysRevB.103.035419. NRG Ljubljana was used to compute subgap spectra and transport across an impurity coupled to phase-biased superconducting and metallic reservoirs.

  • Multichannel charge Kondo effect and non-Fermi-liquid fixed points in conventional and topological superconductor islands. Michał Papaj, Zheng Zhu, and Liang Fu. Physical Review B (2019). doi:10.1103/PhysRevB.99.014512. NRG Ljubljana was used to identify multichannel charge-Kondo fixed points and their non-Fermi-liquid thermodynamics.

  • Tunneling spectroscopy of a single quantum dot coupled to a superconductor: From Kondo ridge to Andreev bound states. J.-D. Pillet, P. Joyez, Rok Žitko, and M. F. Goffman. Physical Review B (2013). doi:10.1103/PhysRevB.88.045101. NRG Ljubljana was used to reproduce the measured evolution from a Kondo resonance to Andreev bound states.

Molecular and surface impurities

  • Individual Assembly of Radical Molecules on Superconductors: Demonstrating Quantum Spin Behavior and Bistable Charge Rearrangement. Chao Li, Vladislav Pokorný, Martin Žonda, Jung-Ching Liu, Ping Zhou, Outhmane Chahib, Thilo Glatzel, Robert Häner, Silvio Decurtins, Shi-Xia Liu, Rémy Pawlak, and Ernst Meyer. ACS Nano (2025). doi:10.1021/acsnano.4c12387. NRG Ljubljana was used to model the interacting molecular states and assign the measured spin and charge-state spectra of radicals on Pb(111).

  • Topological quantum phase transition of nickelocene on Cu(100). Germán G. Blesio, Rok Žitko, Luis O. Manuel, and Armando A. Aligia. SciPost Physics (2023). doi:10.21468/SciPostPhys.14.3.042. NRG Ljubljana was used to solve the two-channel spin-1 impurity model and identify the topological transition observed in the molecular spectra.

  • Iron phthalocyanine on Au(111) is a "non-Landau" Fermi liquid. R. Žitko, G. G. Blesio, L. O. Manuel, and A. A. Aligia. Nature Communications (2021). doi:10.1038/s41467-021-26339-z. NRG Ljubljana was used to solve a multiorbital impurity model and identify the singular Fermi-liquid state of iron phthalocyanine on gold.

  • Magnetically Tuned Kondo Effect in a Molecular Double Quantum Dot: Role of the Anisotropic Exchange. Peter Zalom, Joeri de Bruijckere, Rocco Gaudenzi, Herre S. J. van der Zant, Tomáš Novotný, and Richard Korytár. The Journal of Physical Chemistry C (2019). doi:10.1021/acs.jpcc.9b00783. NRG Ljubljana was used to model anisotropic exchange and the magnetic-field tuning of the molecular Kondo effect.

  • From Kondo to local singlet state in graphene nanoribbons with magnetic impurities. G. S. Diniz, G. I. Luiz, A. Latgé, and E. Vernek. Physical Review B (2018). doi:10.1103/PhysRevB.97.115444. NRG Ljubljana was used to calculate thermodynamic properties and distinguish Kondo screening from local-singlet formation near a nanoribbon edge.

  • Kondo behavior and conductance through 3d impurities in gold chains doped with oxygen. M. A. Barral, S. Di Napoli, G. Blesio, P. Roura-Bas, A. Camjayi, L. O. Manuel, and A. A. Aligia. The Journal of Chemical Physics (2017). doi:10.1063/1.4973982. NRG Ljubljana was combined with first-principles parameters to calculate Kondo behavior and conductance for transition-metal impurities in gold chains.

  • Kondo conductance across the smallest spin 1/2 radical molecule. Ryan Requist, Silvio Modesti, Pier Paolo Baruselli, Alexander Smogunov, Michele Fabrizio, and Erio Tosatti. Proceedings of the National Academy of Sciences (2014). doi:10.1073/pnas.1322239111. NRG Ljubljana was combined with density-functional calculations to model the measured Kondo conductance through a single radical molecule.

DMFT and correlated materials

  • Power-law spectra and asymptotic ω/T scaling in the orbital-selective Mott phase of a three-orbital Hubbard model. Fabian Eickhoff. SciPost Physics (2026). doi:10.21468/SciPostPhys.20.2.050. NRG Ljubljana was used as the DMFT impurity solver to resolve power-law spectra and asymptotic frequency-temperature scaling.

  • Fate of Quasiparticles at High Temperature in the Correlated Metal Sr2RuO4. A. Hunter, S. Beck, E. Cappelli, F. Margot, M. Straub, Y. Alexanian, G. Gatti, M. D. Watson, T. K. Kim, C. Cacho, N. C. Plumb, M. Shi, M. Radović, D. A. Sokolov, A. P. Mackenzie, M. Zingl, J. Mravlje, A. Georges, F. Baumberger, and A. Tamai. Physical Review Letters (2023). doi:10.1103/PhysRevLett.131.236502. NRG Ljubljana was used as a multiorbital DMFT impurity solver to compare temperature-dependent quasiparticle spectra with photoemission data.

  • Mott Quantum Critical Points at Finite Doping. Maria Chatzieleftheriou, Alexander Kowalski, Maja Berović, Adriano Amaricci, Massimo Capone, Lorenzo De Leo, Giorgio Sangiovanni, and Luca de' Medici. Physical Review Letters (2023). doi:10.1103/PhysRevLett.130.066401. A modified NRG Ljubljana solver was used in DMFT to locate quantum critical endpoints of the finite-doping Mott transition.

  • Hund bands in spectra of multiorbital systems. M. Środa, J. Mravlje, G. Alvarez, E. Dagotto, and J. Herbrych. Physical Review B (2023). doi:10.1103/PhysRevB.108.L081102. NRG Ljubljana was used in DMFT calculations that identify Hund-coupling sidebands in multiorbital spectral functions.

  • Off-shell effective energy theory: A unified treatment of the Hubbard model from d = 1 to d = infinity. Zhengqian Cheng and Chris A. Marianetti. Physical Review B (2020). doi:10.1103/PhysRevB.101.081105. NRG Ljubljana supplied DMFT reference solutions used to test the off-shell effective-energy description across dimensions.

  • Real-space dynamical mean-field theory of Friedel oscillations in strongly correlated electron systems. B. Chatterjee, J. Skolimowski, K. Makuch, and K. Byczuk. Physical Review B (2019). doi:10.1103/PhysRevB.100.115118. NRG Ljubljana was used as the site-resolved impurity solver for real-space DMFT calculations of defect-induced Friedel oscillations.

  • Spin-selective localization of correlated lattice fermions. J. Skolimowski, D. Vollhardt, and K. Byczuk. Physical Review B (2015). doi:10.1103/PhysRevB.92.094202. NRG Ljubljana was integrated into DMFT to determine the spin-selective localization transition in correlated lattice fermions.

Methods and benchmarks

  • Auxiliary master equation approach to the Anderson-Holstein impurity problem out of equilibrium. Daniel Werner, Rok Žitko, and Enrico Arrigoni. Physical Review B (2024). doi:10.1103/PhysRevB.109.075156. NRG Ljubljana provided equilibrium reference spectra for benchmarking the auxiliary master-equation treatment of the Anderson-Holstein model.

  • Surrogate model solver for impurity-induced superconducting subgap states. Virgil V. Baran, Emil J. P. Frost, and Jens Paaske. Physical Review B (2023). doi:10.1103/PhysRevB.108.L220506. NRG Ljubljana supplied reference subgap spectra used to validate the surrogate-model impurity solver.

  • Kondo physics of the Anderson impurity model by distributional exact diagonalization. S. Motahari, R. Requist, and D. Jacob. Physical Review B (2016). doi:10.1103/PhysRevB.94.235133. NRG Ljubljana supplied benchmark spectral and quasiparticle properties for evaluating distributional exact diagonalization.

  • Padé approximant approach for obtaining finite-temperature spectral functions of quantum impurity models using the numerical renormalization group technique. Žiga Osolin and Rok Žitko. Physical Review B (2013). doi:10.1103/PhysRevB.87.245135. NRG Ljubljana generated imaginary- and real-frequency data used to assess Padé reconstruction of finite-temperature spectra.