Density matrix numerical renormalization group for non-Abelian symmetries

2008/02/29 by A. I. Toth, A. Tóth, C. P. Moca +5 · 4 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum, superfluid, helium dynamics #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.78.245109

published as Phys. Rev. B 78, 245109 (2008) · 12 pages, 6 figures, PRB format

arxiv created 2008/02/29 · openalex publication_date 2008/12/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian local symmetries present in the quantum impurity system. We illustrate the benefits of using non-Abelian symmetries by the example of calculations for the T matrix of the two-channel Kondo model in the presence of magnetic field, for which conventional NRG methods produce large errors and/or take a long run-time.

Citations

• Numerical renormalization group method for quantum impurity systems
• Transport Coefficients of the Anderson Model via the Numerical Renormalization Group
• Density-matrix algorithms for quantum renormalization groups
• The renormalization group: Critical phenomena and the Kondo problem
• Dynamical conductance in the two-channel Kondo regime of a double dot system
• Real-Time Dynamics in Quantum-Impurity Systems: A Time-Dependent Numerical Renormalization-Group Approach
• A ?fermi-liquid? description of the Kondo problem at low temperatures

Cited by

• A numerical algorithm for the explicit calculation of SU(N) and SL(N,\mathbb C)SL(N,C) Clebsch–Gordan coefficients
• Underscreened Kondo effect in quantum dots coupled to ferromagnetic leads
• Kondo temperature of SU(4) symmetric quantum dots
• Fermionic Orbital Optimization in Tensor Network States

Related

• Manual for the Flexible DM-NRG code
• Numerical renormalization group method for quantum impurity systems
• Numerical renormalization group calculations for magnetic impurity systems with spin-orbit coupling and crystal-field effects
• Matrix-product-state comparison of the numerical renormalization group and the variational formulation of the density-matrix renormalization group
• Auxiliary-Bath Numerical Renormalization Group Method and Successive Collective Screening in Multi-Impurity Kondo Systems