Real-Time Dynamics in Quantum-Impurity Systems: A Time-Dependent Numerical Renormalization-Group Approach

Anders, Frithjof B.; Schiller, Avraham

doi:10.1103/physrevlett.95.196801

Cited by 409 publications

(593 citation statements)

References 18 publications

(49 reference statements)

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“…The tools to do so using NRG have become accessible only rather recently. 10,22,23,26 One considers a sudden change in some local term in the Hamiltonian and studies the subsequent time-evolution, characterized, for example, by the quantity G I |e −iĤFt |G I . Its numerical evaluation requires the calculation of overlaps of eigenstates ofĤ I andĤ F .…”

Section: Discussionmentioning

confidence: 99%

Anderson orthogonality and the numerical renormalization group

2011

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Anderson Orthogonality (AO) refers to the fact that the ground states of two Fermi seas that experience different local scattering potentials, say |GI and |GF , become orthogonal in the thermodynamic limit of large particle number N , in that | GI|GF | ∼ N − 1 2 ∆ 2 AO for N → ∞. We show that the numerical renormalization group offers a simple and precise way to calculate the exponent ∆AO: the overlap, calculated as function of Wilson chain length k, decays exponentially, ∼ e −kα , and ∆AO can be extracted directly from the exponent α. The results for ∆AO so obtained are consistent (with relative errors typically smaller than 1%) with two other related quantities that compare how ground state properties change upon switching from |GI to |GF : the difference in scattering phase shifts at the Fermi energy, and the displaced charge flowing in from infinity. We illustrate this for several nontrivial interacting models, including systems that exhibit population switching.

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Section: Discussionmentioning

confidence: 99%

Anderson orthogonality and the numerical renormalization group

2011

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“…However, the requisite numerical tools are available within NRG, 31,34 and have become very accurate quantitatively due to recent methodological refinements. 15,35,36 NRG, developed in the context of quantum impurity models, offers a very direct way of evaluating the overlap, since it allows both ground states |G i and |G f to be calculated explicitly. Models treatable by NRG have the generic formĤ =Ĥ B +Ĥ d .…”

Section: F Ao Exponents and Nrgmentioning

confidence: 99%

“…To this end, one uses two separate NRG runs to calculate the ground state |G i ofĤ i and an approximate but complete set of eigenstates |n ofĤ f . 35,36 The Lehmann sum in Eq. (26) can then be evaluated explicitly, 37,38 while representing the δ-functions occurring therein using a logGaussian broadening scheme.…”

Section: F Ao Exponents and Nrgmentioning

confidence: 99%

Anderson orthogonality in the dynamics after a local quantum quench

et al. 2012

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We present a systematic study of the role of Anderson orthogonality for the dynamics after a quantum quench in quantum impurity models, using the numerical renormalization group. As shown by Anderson in 1967, the scattering phase shifts of the single-particle wave functions constituting the Fermi sea have to adjust in response to the sudden change in the local parameters of the Hamiltonian, causing the initial and final ground states to be orthogonal. This so-called Anderson orthogonality catastrophe also influences dynamical properties, such as spectral functions. Their low-frequency behaviour shows non-trivial power laws, with exponents that can be understood using a generalization of simple arguments introduced by Hopfield and others for the X-ray edge singularity problem. The goal of this work is to formulate these generalized rules, as well as to numerically illustrate them for quantum quenches in impurity models involving local interactions. As a simple yet instructive example, we use the interacting resonant level model as testing ground for our generalized Hopfield rule. We then analyse a model exhibiting population switching between two dot levels as a function of gate voltage, probed by a local Coulomb interaction with an additional lead serving as charge sensor. We confirm a recent prediction that charge sensing can induce a quantum phase transition for this system, causing the population switch to become abrupt. We elucidate the role of Anderson orthogonality for this effect by explicitly calculating the relevant orthogonality exponents.

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“…Although theoretical physicists devoted a lot of effort to design methods that are able to tackle these difficulties, so far none of the proposed methods proved to be entirely successful in describing strongly interacting non-equilibrium systems: Monte Carlo methods are presently unable to reach the required precision, 20,21 Bethe Ansatz methods can be used for a few models only, and are still in an experimental stage, [22][23][24] and perturbative renormalization group methods can only reach a particular region of the parameter space. [25][26][27][28] Maybe numerical renormalization group methods are currently the most reliable techniques to study these non-equilibrium systems, 24,29,30 however, they scale very badly with the number of states involved, and to compute the transport through just two levels in the presence of interaction seems to be numerically too demanding.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium transport theory of the singlet-triplet transition: Perturbative approach

2010

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We use a simple iterative perturbation theory to study the singlet-triplet (ST) transition in lateral and vertical quantum dots, modeled by the non-equilibrium two-level Anderson model. To a great surprise, the region of stable perturbation theory extends to relatively strong interactions, and this simple approach is able to reproduce all experimentally-observed features of the ST transition, including the formation of a dip in the differential conductance of a lateral dot indicative of the two-stage Kondo effect, or the maximum in the linear conductance around the transition point. Choosing the right starting point to the perturbation theory is, however, crucial to obtain reliable and meaningful results.

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Real-Time Dynamics in Quantum-Impurity Systems: A Time-Dependent Numerical Renormalization-Group Approach

Cited by 409 publications

References 18 publications

Anderson orthogonality and the numerical renormalization group

Anderson orthogonality and the numerical renormalization group

Anderson orthogonality in the dynamics after a local quantum quench

Nonequilibrium transport theory of the singlet-triplet transition: Perturbative approach

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