Numerical renormalization-group computation of specific heats

Costa, Sandra; Paula, C. A.; Líbero, Valter Luiz; Oliveira, L. N.

doi:10.1103/physrevb.55.30

Cited by 22 publications

(13 citation statements)

References 31 publications

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“…4 shows that the Kondo peak covers an entropy Sϭk B ln 2, as expected ͑see Ref. 13, and references therein͒. The second peak in the specific heat covers an entropy k B ln 8, including the contribution of the eight atomic levels that lie below the Fermi energy.…”

Section: ͑314͒supporting

confidence: 79%

Thermodynamics of the Anderson lattice

Bernhard

Lacroix

1999

Phys. Rev. B

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The periodic Anderson model is considered in a cubic lattice at half filling in the paramagnetic and antiferromagnetic phases. A Green's-function approximation is introduced that involves a self-consistent evaluation of the f-electron concentration and the sublattice magnetization. The Néel and Kondo temperatures are evaluated as a function of the model parameters. We obtain a simple description of the pressure phase diagram of heavy fermion compounds. The specific heat is calculated as a function of temperature at different points of the phase diagram.

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Section: ͑314͒supporting

confidence: 79%

Thermodynamics of the Anderson lattice

Bernhard

Lacroix

1999

Phys. Rev. B

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“…These may be a fixed number N keep of the lowest energy states, or one may specify a predefined m 0 , and retain only those states with rescaled energies (E m p −E m GS )/t m (z) < e c (Λ), where E m GS is the (absolute) groundstate energy at iteration m and e c (Λ) is Λ-dependent cut-off energy. 31,33,34 For most results in this paper, we used m 0 = 4, 5, respectively for H, H 0 , and e c (Λ) = 15 √ Λ ≈ 47 for Λ = 10 and found excellent agreement with exact continuum results from Bethe ansatz (after appropriate z-averaging, see below). Calculations at smaller Λ = 4, using m 0 = 5, 6 for H, H 0 , respectively, and e c (Λ) = 40 were also carried out for the local susceptibility in Sec.…”

Section: Model Methods and Conventional Approach To Thermodynamicsmentioning

confidence: 66%

Full density-matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model

2012

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Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models [see A. Weichselbaum and J. von Delft, Phys. Rev. Lett. 99, 076402 (2007)] by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller [F. B. Anders and A. Schiller, Phys. Rev. Lett. 95, 196801 (2005)]. While these developments prove particularly useful in the calculation of transient response and finite-temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to the Anderson impurity model. We compare the results for the susceptibility and specific heat to both the conventional approach within NRG and to exact Bethe ansatz results. We also point out a subtlety in the calculation of the susceptibility (in a uniform field) within the FDM approach. Finally, we show numerically that for the Anderson model, the susceptibilities in response to a local and a uniform magnetic field coincide in the wide-band limit, in accordance with the Clogston-Anderson compensation theorem.

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“…Next, the logarithmic discretization of the conduction band is carried out according to one of the available discretization schemes 63,64,[79][80][81][82] by dividing the integration range [−1, 1] into standard intervals I ± m and using the following weight function on the m th positive and negative interval, respectively:…”

Section: Appendix A: Numerical Renormalization Group Calculations Witmentioning

confidence: 99%

Numerical renormalization group calculations of the magnetization of Kondo impurities with and without uniaxial anisotropy

Höck

Schnack

2013

Phys. Rev. B

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We study a Kondo impurity model with additional uniaxial anisotropy D in a nonzero magnetic field B using the numerical renormalization group (NRG). The ratio g e /g S of electron and impurity g factor is regarded as a free parameter and, in particular, the special cases of a "local" (g e = 0) and "bulk" (g e = g S ) field are considered. For a bulk field, the relationship between the impurity magnetization M and the impurity contribution to the magnetization M imp is investigated and it is shown that M and M imp are proportional to each other for fixed coupling strength. Furthermore, we find that the g-factor ratio effectively rescales the magnetic field argument of the zero-temperature impurity magnetization. In case of an impurity with D = 0 and g e = g S , it is demonstrated that at zero temperature M(B), unlike M imp (B), does not display universal behavior. With additional "easy-axis" anisotropy, the impurity magnetization is "stabilized" at a D-dependent value for k B T g S μ B B |D| and, for nonzero temperature, is well described by a shifted and rescaled Brillouin function on energy scales that are small compared to |D|. In the case of "hard-axis" anisotropy, the magnetization curves can feature steps which are due to field-induced pseudo-spin-1 2 Kondo effects. For large hard-axis anisotropy and a local field, these screening effects are described by an exchange-anisotropic spin-1 2 Kondo model with an additional scattering term that is spin dependent (in contrast to ordinary potential scattering). In accordance with the observed step widths, this effective model predicts a decrease of the Kondo temperature with every further step that occurs upon increasing the field. Our study is motivated by the question as to how the magnetic properties of a deposited magnetic molecule are modified by the interaction with a nonmagnetic metallic surface.

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Numerical renormalization-group computation of specific heats

Cited by 22 publications

References 31 publications

Thermodynamics of the Anderson lattice

Thermodynamics of the Anderson lattice

Full density-matrix numerical renormalization group calculation of impurity susceptibility and specific heat of the Anderson impurity model

Numerical renormalization group calculations of the magnetization of Kondo impurities with and without uniaxial anisotropy

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