Abstract
In this chapter we set up the basic framework of the flow equation approach to many-particle systems. We will do this by first clarifying the importance of energy scale separation in many-particle systems, and then use this as a guiding principle to develop the flow equation method. The fundamental ideas of the flow equation approach are summed up in Sect. 2.2.4. As a first example for the flow equation approach we solve a simple model in Sect. 2.3 and compare the flow equation solution with the conventional scaling approach.
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References
P.W. Anderson: Basic Notions of Condensed Matter Physics, 6th edn (Addison-Wesley, Reading Mass. 1996)
N. Andrei, K. Furuya, and J.H. Lowenstein, Rev. Mod. Phys. 55, 331 (1983)
A.M. Tsvelick and P.B. Wiegmann, Adv. Phys. 32, 453 (1983)
W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989)
A. Georges, G. Kotliar, W. Krauth, and M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)
A.C. Hewson: The Kondo Problem to Heavy Fermions, 1st edn (Cambridge University Press, Cambridge 1993)
S.D. Głazek and K.G. Wilson, Phys. Rev. D 48, 5863 (1993)
S.D. Głazek and K.G. Wilson, Phys. Rev. D 49, 4214 (1994)
F. Wegner, Ann. Phys. (Leipzig) 3, 77 (1994)
F. Wegner, Phil. Mag. B 77, 1249 (1998)
F. Wegner, Phys. Rep. 348, 77 (2001)
F. Wegner, Nucl. Phys. B (Proc. Suppl.) 90, 141 (2000)
F. Wegner, cond-mat/0511660
S.D. Głazek, Renormalization of Hamiltonians. In: Lecture Notes of the First International School on Light-Cone Quantization (Iowa State University Press, Ames 1997)
T.S. Walhout, Phys. Rev. D 59, 065009 (1999)
S.D. Głazek, Acta Phys. Polon. B 31, 909 (2000)
M.T. Chu and K.R. Driessel, SIAM J. Numer. Anal. 27, 1050 (1990)
M.T. Chu, Fields Institute Communications 3, 87 (1994)
R.W. Brockett, Lin. Alg. and its Appl. 146, 79 (1991)
W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery: Numerical Recipes in C, 2nd edn (Cambridge University Press, Cambridge 1992)
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975)
S.D. Głazek and K.G. Wilson, Phys. Rev. D 57, 3558 (1998)
S.D. Głazek and K.G. Wilson, Phys. Rev. Lett. 89, 230401 (2002); Erratum Phys. Rev. Lett. 92, 139901 (2004)
S.D. Głazek and K.G. Wilson, Phys. Rev. B 69, 094303 (2004)
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Kehrein, S. (2006). Transformation of the Hamiltonian. In: The Flow Equation Approach to Many-Particle Systems. Springer Tracts in Modern Physics, vol 217. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34068-8_2
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DOI: https://doi.org/10.1007/3-540-34068-8_2
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