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The resulting QSpace tensors can deal with any set of abelian symmetries together with arbitrary non-abelian symmetries with compact, i.e. Single-shell and patching schemes L18 17.06.21 NRG IV: Spectral function, fdm-NRG 1. Lehmann representation of spectral function. In the Appendix A Non-abelian symmetries 101, Appendix B Numerical implementation, Appendix C Example, finally, an extensive introduction to non-abelian symmetries is given for practical applications, together with simple self-contained numerical procedures to obtain Clebsch–Gordan coefficients and irreducible operators sets. L17 16.06.21 NRG III: Thermodynamics, Lehmann 1. These are compared in detail, including their respective dramatic gain in numerical efficiency. FBK, S-SBL,and JvD are supported by the Deutsche Forschungsge-meinschaft under Germany’s Excellence StrategyEXC-2111390814868 S-SBL further by Grant. The same system is analyzed using several alternative symmetry scenarios based on combinations of U ( 1 ) charge, SU ( 2 ) spin, SU ( 2 ) charge, SU ( 3 ) channel, as well as the enveloping symplectic Sp ( 6 ) symmetry. The NRG results were obtained usingthe QSpace tensor library 80, 81, and TRIQS applica-tions 8284 were used see 50 for details.
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A detailed analysis is presented for a fully screened spin- 3/2 three-channel Anderson impurity model in the presence of conservation of total spin, particle–hole symmetry, and SU ( 3 ) channel symmetry. In this paper, the focus is on the application of the non-abelian framework within the NRG. The unifying tensor-representation for quantum symmetry spaces, dubbed QSpace, is particularly suitable to deal with standard renormalization group algorithms such as the numerical renormalization group (NRG), the density matrix renormalization group (DMRG), or also more general tensor networks such as the multi-scale entanglement renormalization ansatz (MERA). The two crucial ingredients, the Clebsch–Gordan algebra for multiplet spaces as well as the Wigner–Eckart theorem for operators, are accounted for in a natural, well-organized, and computationally straightforward way. You may have to select a menu option or click a button.A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of well-defined orthonormal local as well as effective basis sets. Follow the instructions for disabling the ad blocker on the site you’re viewing.You may have more than one ad-blocker installed. You’ll usually find this icon in the upper right-hand corner of your screen. Click the icon of the ad-blocker extension installed on your browser.When it turns gray, click the refresh icon that has appeared next to it or click the button below to continue.Click on the large blue power icon at the top.Click the UBlock Origin icon in the browser extension area in the upper right-hand corner.
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