Tensor networks and the numerical renormalization group

Abstract

The full-density-matrix numerical renormalization group (NRG) has evolved as a systematic and transparent setting for the cal- culation of thermodynamical quantities at arbitrary temperatures within the NRG framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets intro- duced by Anders and Schiller (2005). In addition, specific attention is given to the possible feedback from low energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-Golden rule calculations (fgrNRG), as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.

20 pages, 11 figures (adapted from habilitation thesis)

References in corpus (28)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Theory of ultracold Fermi gases
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• The numerical renormalization group method for quantum impurity systems
• Real time evolution using the density matrix renormalization group
• Area laws in quantum systems: mutual information and correlations
• Repulsively bound atom pairs in an optical lattice
• From density-matrix renormalization group to matrix product states
• Entropy scaling and simulability by Matrix Product States
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Energy resolution and discretization artefacts in the numerical renormalization group
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Atomic three-body loss as a dynamical three-body interaction
• Ultrafast optical control of entanglement between two quantum dot spins
• Chebyshev matrix product state approach for spectral functions
• Implementing global Abelian symmetries in projected entangled-pair state algorithms
• A numerical algorithm for the explicit calculation of SU(N) and SL(N,C) Clebsch-Gordan coefficients
• Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
• Kondo decoherence: finding the right spin model for iron impurities in gold and silver
• Density matrix numerical renormalization group for non-Abelian symmetries
• Strong enhancement of transport by interaction on contact links
• Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization group
• High Energy Dynamics of the Single Impurity Anderson Model
• Absorption and Emission in quantum dots: Fermi surface effects of Anderson excitons
• SU(3) Anderson impurity model: A numerical renormalization group approach exploiting non-Abelian symmetries

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• Local susceptibility and Kondo scaling in the presence of finite bandwidth
• Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling
• A beginner's guide to non-abelian iPEPS for correlated fermions
• Iron impurities in gold and silver: Comparison of transport measurements to numerical renormalization group calculations exploiting non-Abelian symmetries
• Differentiating Hund from Mott physics in a three-band Hubbard-Hund model: Temperature dependence of spectral, transport, and thermodynamic properties
• RG transport theory for open quantum systems: Charge fluctuations in multilevel quantum dots in and out of equilibrium
• Manipulating Non-Abelian Anyons in a Chiral Multichannel Kondo Model
• QSpace - An open-source tensor library for Abelian and non-Abelian symmetries
• Non-Fermi liquid behavior in transport through Co doped Au chains
• Machine learning of Kondo physics using variational autoencoders and symbolic regression
• Filling-driven Mott transition in SU(N) Hubbard models
• Uncovering Non-Fermi-Liquid Behavior in Hund Metals: Conformal Field Theory Analysis of an SU(2)$\times$SU(3) Spin-Orbital Kondo Model
• Universal Thermal Entanglement of Multichannel Kondo Effects
• Equilibrium Fermi-liquid coefficients for the fully screened N-channel Kondo model
• Complex Time Evolution in Tensor Networks
• Numerical renormalization group method for entanglement negativity at finite temperature
• Real-frequency quantum field theory applied to the single-impurity Anderson model
• Projector formalism for kept and discarded spaces of matrix product states
• Quench dynamics of correlated quantum dot proximitized to superconducting lead
• Non-Fermi liquid behaviour in non-equilibrium transport through Co doped Au chains connected to four-fold symmetric leads
• Proposed Rabi-Kondo Correlated State in a Laser-Driven Semiconductor Quantum Dot
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• The Ohmic two-state system from the perspective of the interacting resonant level model: Thermodynamics and transient dynamics
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• Low-temperature behavior of transmission phase shift across a Kondo correlated quantum dot
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• Thermalization and dynamics in the single impurity Anderson model
• Dynamical correlation functions from complex time evolution
• Symmetric improved estimators for multipoint vertex functions
• Flavor fluctuations in 3-level quantum dots: Generic SU(3)-Kondo fixed point in equilibrium and non-Kondo fixed points in nonequilibrium
• Low-energy perspective on two-orbital Hund metals and the case of LaNiO2
• Fermi-Liquid $T^2$ Resistivity: Dynamical Mean-Field Theory Meets Experiment
• Chiral numerical renormalization group
• Vacancy-induced tunable Kondo effect in twisted bilayer graphene
• Nonmonotonic buildup of spin-singlet correlations in a double quantum dot
• Testing the parquet equations and the U(1) Ward identity for real-frequency correlation functions from the multipoint numerical renormalization group
• Low-temperature transport in high-conductivity correlated metals: a density-functional plus dynamical mean-field study of cubic perovskites
• RKKY to Kondo crossover in Helical Edge of a Topological Insulator
• Equilibrium Dynamics of the Sub-Ohmic Spin-boson Model At Finite Temperature
• Dynamical Spectral Function From Numerical Renormalization Group: A Full Excitation Approach
• Oscillate and Renormalize: Fast Phonons Reshape the Kondo Effect in Flat Band Systems
• Time-dependent spintronic anisotropy in magnetic molecules
• Spin-charge Kondo effect for a quantum dot with side coupled Majorana zero mode
• Rainbow chains and numerical renormalisation group for accurate chiral conformal spectra
• Compressing local vertex functions from the multipoint numerical renormalization group using quantics tensor cross interpolation
• Computing local multipoint correlators using the numerical renormalization group
• Non-Fermi-liquid Kondo screening under Rabi driving
• Improved estimator for numerical renormalization group calculations of the self-energy