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arXiv:cond-mat/0408416

Spectral Function for the Anderson Model based on Nonequilibrium Perturbation Theory

Mami Hamasaki

Published Aug 19, 2004• 0 citations
arXivHTMLPDF

Abstract

The paper has been withdrawn. The revised version is shown as cond-mat/0506752 and published in Condensed Matter Physics, vol.10, No.2(50)235-248(2007) (Lviv, Ukraine).
DOI
10.48550/arxiv.cond-mat/0408416

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conferred him PhD degree after successful defense of PhD thesis entitled "Statistical theory of partially excited systems", which Oleg elaborated under the guidance of Professor Ihor Yukhnovskii and Professor Roman Levitskii.Over the past few decades Oleg Derzhko has been scientifically working at the Institute for Condensed Matter Physics of National Academy of Sciences of Ukraine in Lviv, at first, as a research associate at the former Lviv Division of the Institute for Theoretical Physics of the Academy of Sciences of the UkrSSR (since 1982), and finally as head of Department for Theory of Model Spin Systems (2003-2016) and head of Department for Quantum Statistics (since 2016 up till now).During this period, he has also performed a long-term lecturing of several courses of theoretical physics at Ivan Franko National University in Lviv and Lviv Polytechnic National University.Oleg's scientific interests cover various modern problems of condensed matter physics and statistical physics.At the Institute for Condensed Matter Physics in Lviv OlegDerzhko has successfully developed a research direction, which is primarily focused on the state-of-theart problems of quantum spin models with a particular emphasis on the exactly solvable models and is already recognized worldwide.In addition to this challenging research topic in its own right, Oleg has a lot of other scientific interests including, but not limited to, unsolved problems of phase transitions of atomic liquids.It is impossible to summarize here all Oleg's achievements, so let us briefly review at least a few most important milestones of his scientific career.Early-career scientific contributions of Oleg Derzhko were devoted to equilibrium properties of partially excited gas and an influence of resonance irradiation upon a liquid-gas phase transition [1].He did not stop taking interest in this topic across his entire scientific career.The further research in this direction has been developing mainly in collaboration with Dr. Vasyl Myhal where their joint efforts are focused on the properties of a two-phase fluid of two-level atoms, the part of which is excited.Among other matters, Oleg and Vasyl brought a deeper understanding into the vapor-to-liquid transition, wetting under electromagnetic resonance irradiation, a microscopic theory of photonucleation with the special emphasis laid on nucleation phenomena in an electric field, surface tension, cavitation and so on [2][3][4].Exactly solvable problems in general and particularly one-dimensional quantum XY models and quantum Ising models in a transverse magnetic field have apparently become Oleg's greatest scientific passion and delight, where he substantially extended the rigorous results with the help of Jordan-Wigner fermionization technique [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].To this end, Oleg Derzhko and his collaborators, which were predominantly from the Institute for Condensed Matter Physics in Lviv, have nontrivially adapted the recipé originally envisaged in a seminal paper by Lieb, Schultz, and Mattis [20].A big step forward at that time was the formulation of the exact numerical method for the calculation of time-dependent spin correlation functions and the corresponding structure factors [5][6][7].Exact solutions for numerous random and periodic non-uniform versions of quantum XY and Ising models achieved by Oleg and by his research group brought a considerable progress in theoretical understanding of a lot of exciting phenomena emergent in one-dimensional quantum spin chains.For instance, in this field of study Oleg has significantly contributed to a clarification of the effect of regular nonuniformity, randomness and correlated disorder on static and dynamical properties of several exactly solved quantum XY and Ising chains [8][9][10][11][12][13][14].Oleg achieved another important breakthrough in this research area by a detailed examination of spin-Peierls instabilities of a certain class of quantum XY chains [15][16][17], as well as, quantum phase transitions and the dynamics of exactly solved XY chains with three-site interactions [16,18,19].

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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.
conferred him PhD degree after successful defense of PhD thesis entitled "Statistical theory of partially excited systems", which Oleg elaborated under the guidance of Professor Ihor Yukhnovskii and Professor Roman Levitskii.Over the past few decades Oleg Derzhko has been scientifically working at the Institute for Condensed Matter Physics of National Academy of Sciences of Ukraine in Lviv, at first, as a research associate at the former Lviv Division of the Institute for Theoretical Physics of the Academy of Sciences of the UkrSSR (since 1982), and finally as head of Department for Theory of Model Spin Systems (2003-2016) and head of Department for Quantum Statistics (since 2016 up till now).During this period, he has also performed a long-term lecturing of several courses of theoretical physics at Ivan Franko National University in Lviv and Lviv Polytechnic National University.Oleg's scientific interests cover various modern problems of condensed matter physics and statistical physics.At the Institute for Condensed Matter Physics in Lviv OlegDerzhko has successfully developed a research direction, which is primarily focused on the state-of-theart problems of quantum spin models with a particular emphasis on the exactly solvable models and is already recognized worldwide.In addition to this challenging research topic in its own right, Oleg has a lot of other scientific interests including, but not limited to, unsolved problems of phase transitions of atomic liquids.It is impossible to summarize here all Oleg's achievements, so let us briefly review at least a few most important milestones of his scientific career.Early-career scientific contributions of Oleg Derzhko were devoted to equilibrium properties of partially excited gas and an influence of resonance irradiation upon a liquid-gas phase transition [1].He did not stop taking interest in this topic across his entire scientific career.The further research in this direction has been developing mainly in collaboration with Dr. Vasyl Myhal where their joint efforts are focused on the properties of a two-phase fluid of two-level atoms, the part of which is excited.Among other matters, Oleg and Vasyl brought a deeper understanding into the vapor-to-liquid transition, wetting under electromagnetic resonance irradiation, a microscopic theory of photonucleation with the special emphasis laid on nucleation phenomena in an electric field, surface tension, cavitation and so on [2][3][4].Exactly solvable problems in general and particularly one-dimensional quantum XY models and quantum Ising models in a transverse magnetic field have apparently become Oleg's greatest scientific passion and delight, where he substantially extended the rigorous results with the help of Jordan-Wigner fermionization technique [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].To this end, Oleg Derzhko and his collaborators, which were predominantly from the Institute for Condensed Matter Physics in Lviv, have nontrivially adapted the recipé originally envisaged in a seminal paper by Lieb, Schultz, and Mattis [20].A big step forward at that time was the formulation of the exact numerical method for the calculation of time-dependent spin correlation functions and the corresponding structure factors [5][6][7].Exact solutions for numerous random and periodic non-uniform versions of quantum XY and Ising models achieved by Oleg and by his research group brought a considerable progress in theoretical understanding of a lot of exciting phenomena emergent in one-dimensional quantum spin chains.For instance, in this field of study Oleg has significantly contributed to a clarification of the effect of regular nonuniformity, randomness and correlated disorder on static and dynamical properties of several exactly solved quantum XY and Ising chains [8][9][10][11][12][13][14].Oleg achieved another important breakthrough in this research area by a detailed examination of spin-Peierls instabilities of a certain class of quantum XY chains [15][16][17], as well as, quantum phase transitions and the dynamics of exactly solved XY chains with three-site interactions [16,18,19].