Recursive computation of matrix elements in the numerical renormalization group

Pinto, J. W. M.; Oliveira, L. N.

doi:10.1016/j.cpc.2014.01.004

Cited by 5 publications

(6 citation statements)

References 23 publications

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“…It can be applied to systems where a quantum mechanical impurity is coupled to a non-interacting bath of fermions or bosons [29]. There is extensive literature on NRG concepts [4], and numerical implementations [30]. For this reason, this section presents an overview of the method, focused on aspects that distinguish the two approaches.…”

Section: Modified Numerical Renormalization Group Methodsmentioning

confidence: 99%

“…From the practical perspective, the truncation is valuable because it allows iterative diagonalization of the Hamiltonian, a procedure detailed in Ref. [30]. At iteration N (n = 0, 1, .…”

Section: B Truncationmentioning

confidence: 99%

“…This is a relatively simple task, since the iterative diagonalization of the truncated Hamiltonian (48) determines the eigenvalues, and the recursive procedure introduced in Ref. [30] gives immediate access to the matrix elements on the right-hand side of Eq. (63).…”

Section: Energy Momentsmentioning

confidence: 99%

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Real-space numerical renormalization-group computation of transport properties in the side-coupled geometry

Ferrari¹,

Oliveira²

2021

Preprint

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The equilibrium transport properties of an elementary nanostructured device with side-coupled geometry are computed and related to universal functions. The computation relies on a real-space formulation of the numerical renormalization-group (NRG) procedure. The real-space construction, dubbed eNRG, is more straightforward than the NRG discretization and allows more faithful description of the coupling between quantum dots and conduction states. The procedure is applied to an Anderson-model description of a quantum wire side-coupled to a single quantum dot. A gate potential controls the dot occupation. In the Kondo regime, the electrical conductance through this device is known to map linearly onto a universal function of the temperature scaled by the Kondo temperature. Here, the energy moments from which the Seebeck coefficient and the thermal conductance can be computed are shown to map linearly onto universal functions also. The moments and transport properties computed by the eNRG procedure are shown to agree very well with these analytical developments. Algorithms facilitating comparison with experimental results are discussed. As an illustration, one of the algorithms is applied to thermal dependence of the thermopower measured by Köhler [PhD Thesis, TUD, Dresden, 2007] in Lu 0.

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Section: Modified Numerical Renormalization Group Methodsmentioning

confidence: 99%

“…From the practical perspective, the truncation is valuable because it allows iterative diagonalization of the Hamiltonian, a procedure detailed in Ref. [30]. At iteration N (n = 0, 1, .…”

Section: B Truncationmentioning

confidence: 99%

See 1 more Smart Citation

Real-space numerical renormalization-group computation of transport properties in the side-coupled geometry

Ferrari¹,

Oliveira²

2021

Preprint

Self Cite

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show abstract

“…Usually to prevent the rapid growth of the Fock space the states with energies above of E cut Λ −1/2 are discarded, and only the states with lowest many-particle energies are kept, typically E cut ≈ 20 × D. 169 After this, the number of iteration, N , is incremented up to reach the maximun size of the Wilson chain, N max , where typical values are between 60 and 80. 169,170 Finally, with the eigenvector and eigenvalue converged the properties of the system can be analyzed.…”

Section: Appendix Appendix B -Higher-energy Structuresmentioning

confidence: 99%

“…To get around this point, let us empoly the Numerical Renormalization Group (NRG). 41,42,169,170 Describing accurately the coupling between nuclear and electronic movement is the second challenge, and it can be overcome within the Exact Factorization framework.…”

Section: Sticking Coefficientmentioning

confidence: 99%