# Computing Local Multipoint Correlators Using the Numerical Renormalization Group

@article{Lee2021ComputingLM, title={Computing Local Multipoint Correlators Using the Numerical Renormalization Group}, author={Seung-Sup B. Lee and Fabian B. Kugler and Jan von Delft}, journal={Physical Review X}, year={2021} }

Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the non-perturbative, accurate computation of multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. In an accompanying paper, we introduce generalized spectral representations for multipoint correlators. Here, we develop a numerical renormalization group (NRG) approach, capable of efficiently evaluating…

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## References

SHOWING 1-10 OF 182 REFERENCES

Multipoint Correlation Functions: Spectral Representation and Numerical Evaluation

- PhysicsPhysical Review X
- 2021

The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals…

Antiferromagnetic and
d
-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group

- PhysicsPhysical Review B
- 2019

Using the dynamical mean-field theory (DMFT) as a `booster-rocket', the functional renormalization group (fRG) can be upgraded from a weak-coupling method to a powerful computation tool for strongly…

One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT

- Physics
- 2013

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of…

Numerical renormalization group method for quantum impurity systems

- Physics
- 2008

In the early 1970s, Wilson developed the concept of a fully nonperturbative renormalization group transformation. When applied to the Kondo problem, this numerical renormalization group (NRG) method…

Anderson orthogonality in the dynamics after a local quantum quench

- Physics
- 2012

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…

Ab initio dynamical vertex approximation

- Physics
- 2016

Diagrammatic extensions of dynamical mean field theory (DMFT) such as the dynamical vertex approximation (D$\Gamma$A) allow us to include non-local correlations beyond DMFT on all length scales and…

Improved Estimators for the Self-Energy and Vertex Function in Hybridization Expansion Continuous-Time Quantum Monte Carlo Simulations

- Physics
- 2012

measurement procedure for the self-energy and vertex function of the Anderson impurity model within the hybridization expansion continuous-time quantum Monte Carlo algorithm. The method is based on…

Continuous-time quantum Monte Carlo calculation of multiorbital vertex asymptotics

- Physics
- 2017

We derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multi-orbital impurity model. These relate the asymptotics for a general local…

w2dynamics: Local one- and two-particle quantities from dynamical mean field theory

- PhysicsComput. Phys. Commun.
- 2019

Correlated starting points for the functional renormalization group

- Physics
- 2015

We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow.…