In the recent preprints the authors claim that conclusions on the violation of the Luttinger sum rule (LSR) as put forward in published papers by the present authors are false or at least not conclusive enough. It concerns the validity of the LSR within the Mott-Hubbard insulator as manifested in the 1D model of spinless fermions, and the Hubbard model on a triangular lattice. We show below that arguments against the presented analysis are rather easily rejected while still the general question of the validity and breakdown of the LSR remains to be answered.In the recent preprints the authors claim that conclusions on the violation of the Luttinger sum rule (LSR) as put forward in published papers by the present authors are false or at least not conclusive enough. It concerns the validity of the LSR within the Mott-Hubbard insulator as manifested in the 1D model of spinless fermions, and the Hubbard model on a triangular lattice. We show below that arguments against the presented analysis are rather easily rejected while still the general question of the validity and breakdown of the LSR remains to be answered.

arXiv:1002.3732Feb 19, 20100 citations

Addition Theorems

Edgard Elbaz

Springer eBooksJan 1, 19980 citations

On Additivity Questions

Keiji Matsumoto

Springer eBooksSep 14, 20062 citations

Some clarifications on cond-mat/0508763 by M. I. Katsnelson

M. Feldbacher, Ryotaro Arita, Karsten Held +1 more

Katsnelson submitted his Comment on our paper "Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory" to Phys. Rev. Lett. in May 2005. We proved in our report that this comment was incorrect since there is no orthogonality catastrophe for our calculation in Phys. Rev. Lett. 93, 136405 (2004) which is for half-filling. Now in cond-mat/0508763, Katsnelson incorporates our proof of the invalidity of his original Comment, based on Friedel's sum rule. Instead, he now claims that the projective quantum Monte Carlo method is "unpractical" off half-filling, overlooking that our calculations off half-filling (R. Arita and K. Held, LT24 conference proceedings and cond-mat/0508639) employ in practice a noninteracting trial Hamiltonian with the same electron density as the interacting Hamiltonian so that there is again no orthogonality catastrophe. Note added. In the revised version of his comment, Katsnelson gives proper credit to our proof. In our reply, we will present the original proof based on the Friedel sum rule. Moreover, we show that the orthogonality catastrophe does not affect our results. Katsnelson's objection is not valid.Katsnelson submitted his Comment on our paper "Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory" to Phys. Rev. Lett. in May 2005. We proved in our report that this comment was incorrect since there is no orthogonality catastrophe for our calculation in Phys. Rev. Lett. 93, 136405 (2004) which is for half-filling. Now in cond-mat/0508763, Katsnelson incorporates our proof of the invalidity of his original Comment, based on Friedel's sum rule. Instead, he now claims that the projective quantum Monte Carlo method is "unpractical" off half-filling, overlooking that our calculations off half-filling (R. Arita and K. Held, LT24 conference proceedings and cond-mat/0508639) employ in practice a noninteracting trial Hamiltonian with the same electron density as the interacting Hamiltonian so that there is again no orthogonality catastrophe. Note added. In the revised version of his comment, Katsnelson gives proper credit to our proof. In our reply, we will present the original proof based on the Friedel sum rule. Moreover, we show that the orthogonality catastrophe does not affect our results. Katsnelson's objection is not valid.

arXiv:cond-mat/0509443Sep 16, 20050 citations

On Additivity Questions

Keiji Matsumoto

Springer eBooksJun 15, 20060 citations

Tunneling density of states, correlation energy, and spin polarization in the fractional quantum Hall regime

Gaurav Chaudhary, Dmitry K. Efimkin, Allan H. MacDonald

We derive exact sum rules that relate the tunneling density-of-states of spinful electrons in the fractional quantum Hall regime to the spin-dependent many-body ground-state correlation energy. Because the tunneling process is spin-conserving, the two-dimensional (2D) to 2D tunneling current $I$ at a given bias voltage $V$ in a spin-polarized system is a sum of majority and minority spin contributions. The sum rules can be used to define spin-dependent gaps that we associate with peaks in 2D to 2D tunneling $I\text{\ensuremath{-}}V$ curves. We comment in the light of our sum rules on what recent tunneling experiments say about the spin-dependence of correlation energy contributions and propose new measurements that could provide more specific experimental estimates.We derive exact sum rules that relate the tunneling density-of-states of spinful electrons in the fractional quantum Hall regime to the spin-dependent many-body ground-state correlation energy. Because the tunneling process is spin-conserving, the two-dimensional (2D) to 2D tunneling current $I$ at a given bias voltage $V$ in a spin-polarized system is a sum of majority and minority spin contributions. The sum rules can be used to define spin-dependent gaps that we associate with peaks in 2D to 2D tunneling $I\text{\ensuremath{-}}V$ curves. We comment in the light of our sum rules on what recent tunneling experiments say about the spin-dependence of correlation energy contributions and propose new measurements that could provide more specific experimental estimates.

arXiv:1811.07203Physical review. B./Physical review. BAug 2, 20193 citations

I

at a given bias voltage

V

in a spin-polarized system is a sum of majority and minority spin contributions. The sum rules can be used to define spin-dependent gaps that we associate with peaks in 2D to 2D tunneling $I\text{\ensuremath{-}}V$ curves. We comment in the light of our sum rules on what recent tunneling experiments say about the spin-dependence of correlation energy contributions and propose new measurements that could provide more specific experimental estimates.