Effective models for Anderson impurity and Kondo problems from continuous unitary transformations

Krones, Jörn; Uhrig, Götz S.

doi:10.1103/physrevb.91.125102

Cited by 9 publications

(8 citation statements)

References 45 publications

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“…In the solid-state physics literature, the approach is also known as continuous unitary transformation (CUT) theory, see [65][66][67][68][69]. When we discuss our decoupling strategies for the nuclear many-body problem, it will become evident that the IMSRG is related to CC [58,70], canonical transformation theory (CT) [71][72][73], and the Irreducible (or Anti-Hermitian) Contracted Schrödinger Equation (ICSE) approach [74][75][76][77][78][79][80], and there is even some overlap with purely variational methods (see section 4.3).…”

Section: Introductionmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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Abstract. We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band-or block-diagonal form.Exploiting this flexibility, we describe two complementary approaches for the description of closed-and open-shell nuclei: The first is the Multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of nonempirical valence-space interactions that can be used as input for nuclear Shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+Shell model approach provides immediate access to excitation spectra, transitions, etc., but is limited in applicability by the factorial cost of the CI calculations.We review applications of the MR-IMSRG and IMSRG+Shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground-and excited state properties of neon isotopes.Submitted to: Phys. Scr.

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Section: Introductionmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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“…One of such approaches was the so called poor man's scaling, pioneered by Anderson [3]. Models, similar to the one mentioned above, describe magnetic ions in a crystalline electric field [4,5], tunnelling centres [6] and system of quantum dots [7][8][9][10][11][12][13]. It is known that the anisotropy can substantially change the physics of the model in comparison with the isotropic case [14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Poor man’s scaling and Lie algebras

Kogan

2019

J. Phys. Commun.

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We consider a general model, describing a quantum impurity with degenerate energy levels, interacting with a gas of itinerant electrons, derive general scaling equation for the model, and analyse the connection between its particular forms and the symmetry of interaction. On the basis of this analysis we write down scaling equations for the Hamiltonians which are the direct products of su(3) Lie algebras and have either SU(2)×U(1) or SU(2) symmetry. We also put into a new context anisotropic Coqblin-Schrieffer models proposed by us earlier.The scaling equation in this case isThe J z term in the interaction (32) is identical to that in equations (28) and (31). For N=3, the interaction, being expressed through the generators, is V J G J ( ) (the index DM standing for Dzyaloshinskii-Moriya). Using equation (6), we get the scaling equation as dJ d J J dJ d J J dJ d J J ln 2

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“…The single-impurity Kondo and Anderson models and their generalizations to include orbital degeneracy serve as testing grounds for methods that are aimed at the corresponding lattice problems. The Bethe ansatz solutions to the impurity models in turn provide benchmarks [1][2][3][4][5] for ground state and finite-temperature thermodynamic quantities. The numerical solution to the thermodynamic Bethe ansatz (TBA) equations is able to render the full crossover between local-moment behavior at high temperatures and Fermi-liquid behavior at low temperatures with relatively little numerical effort.…”

Section: Introductionmentioning

confidence: 99%

Crystal fields and Kondo effect: New results for the magnetic susceptibility

Desgranges¹

2015

Physica B: Condensed Matter

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a b s t r a c tThe water quality of Feng-qing Lake, which is a landscape lake supplemented with reclaimed water, was surveyed to investigate the relationship between phytoplankton and environmental variables. A total of 29 water samples were collected to analyze temporal variations of phytoplankton and environmental factors from July 2013 to June 2014. Six phyla and 39 genera of phytoplankton were identified when the lake was supplied with reclaimed water. Among these, Cyanophyta and Chlorophyta account for 38.46% and 30.77% of phytoplankton, respectively. The dominant species in the lake are Pseudanabaena limnetica and Chlorella vulgaris, which are present the entire year. Other leading species include Cosmarium sp. and Raphidiopsis curvata. Principal component analysis (PCA) was conducted to analyze the relationship among environmental factors. Canonical correspondence analysis (CCA) was performed to investigate the relationship between environment factors and dominant species. The PCA result showed that temperature (T), total phosphorus (TP), total nitrogen (TN), transparency, and dissolved oxygen are the main factors that affect the eutrophication level of the lake. The CCA result revealed that TN, PO 4 3− -P, chemical oxygen demand (COD), T, and chlorophyll a exhibit a close relation with dominant species. In particular, TN, salinity, and COD influence the growth of P. limnetica; T and COD influence the growth of R. curvata; and T, PO 4 3− -P, NH 3 -N, and pH influence the growth of C. vulgaris and Cosmarium sp.

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Effective models for Anderson impurity and Kondo problems from continuous unitary transformations

Cited by 9 publications

References 45 publications

In-medium similarity renormalization group for closed and open-shell nuclei

In-medium similarity renormalization group for closed and open-shell nuclei

Poor man’s scaling and Lie algebras

Crystal fields and Kondo effect: New results for the magnetic susceptibility

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