Numerical renormalization group for impurity quantum phase transitions: structure of critical fixed points

Lee, Hyunjung; Bulla, Ralf; Vojta, Matthias

doi:10.1088/0953-8984/17/43/012

Cited by 9 publications

(17 citation statements)

References 31 publications

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“…For values of the exponent r > 0, corresponding to a soft-gap in ∆(ω), there are less degrees of freedom available to screen the moment and a quantum phase transition occurs at some finite value of ∆ 0 . This quantum phase transition and the physical properties in the whole parameter regime have been studied in detail with a variety of techniques (for an overview, see ; and the introductory parts in Lee et al (2005)). The NRG method has been particularly helpful to clarify the physics of the soft-gap Anderson model (and the related Kondo version of the model) as we shall briefly discuss in the following.…”

Section: Local Criticalitymentioning

confidence: 99%

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Numerical renormalization group method for quantum impurity systems

2008

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In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG has been later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method including some guidelines of how to calculate physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean field theory.

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Section: Local Criticalitymentioning

confidence: 99%

“…The interacting fixed point of the symmetric soft-gap model has been further analyzed in Lee et al (2005). The general idea of this work can be best explained with Fig.…”

Section: Local Criticalitymentioning

confidence: 99%

Numerical renormalization group method for quantum impurity systems

2008

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“…Since the propagators G σ (ω, h) and G Aσ (ω, |h|) are coincident, so too (trivially) are the associated self-energies (eqs. 3,20)…”

Section: Structure Of Propagatorsmentioning

confidence: 99%

Common non-Fermi liquid phases in quantum impurity physics

2014

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We study correlated quantum impurity models which undergo a local quantum phase transition (QPT) from a strong coupling, Fermi liquid phase to a non-Fermi liquid phase with a globally doubly degenerate ground state. Our aim is to establish what can be shown exactly about such `local moment' (LM) phases; of which the permanent (zero-field) local magnetization is a hallmark, and an order parameter for the QPT. A description of the zero-field LM phase is shown to require two distinct self-energies, which reflect the broken symmetry nature of the phase and together determine the single self-energy of standard field theory. Distinct Friedel sum rules for each phase are obtained, via a Luttinger theorem embodied in the vanishing of appropriate Luttinger integrals. By contrast, the standard Luttinger integral is non-zero in the LM phase, but found to have universal magnitude. A range of spin susceptibilites are also considered; including that corresponding to the local order parameter, whose exact form is shown to be RPA-like, and to diverge as the QPT is approached. Particular attention is given to the pseudogap Anderson model, including the basic physical picture of the transition, the low-energy behavior of single-particle dynamics, the quantum critical point itself, and the rather subtle effect of an applied local field. A two-level impurity model which undergoes a QPT (`singlet-triplet') to an underscreened LM phase is also considered, for which we derive on general grounds some key results for the zero-bias conductance in both phases.Comment: 27 pages, 7 figure

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“…Earlier studies by taking the DOS with a softgap, ρ(ω) ∼ |ω| r (r = 1 for the d-wave superconductor), have shown the existence of a critical coupling, separating the LM and SC phases. 3,[12][13][14][15][16] The present model is more intriguing, as the low-energy excitations in a d-wave superconductor can readily be proliferated by pumping in a supercurrent, which should have a significant control of the impurity state. 17 The purpose of the present work is to demonstrate that a Kosterlitz-Thouless-like IQPT can be realized by tuning the (super-)current.…”

Section: Numerical Resultsmentioning

confidence: 99%

Impurity quantum phase transition in a current-carryingd-wave superconductor

Chen

Yang

et al. 2012

Phys. Rev. B

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We study an Anderson impurity embedded in a d-wave superconductor carrying a supercurrent. The low-energy impurity behavior is investigated by using the numerical renormalization group method developed for arbitrary electronic bath spectra. The results explicitly show that the local impurity state is completely screened upon the non-zero current intensity. The impurity quantum criticality is in accordance with the well-known Kosterlitz-Thouless transition.

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Numerical renormalization group for impurity quantum phase transitions: structure of critical fixed points

Cited by 9 publications

References 31 publications

Numerical renormalization group method for quantum impurity systems

Numerical renormalization group method for quantum impurity systems

Common non-Fermi liquid phases in quantum impurity physics

Impurity quantum phase transition in a current-carryingd-wave superconductor

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