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Exact results for strongly correlate...

Goldbaum, Pedro.

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Exact results for strongly correlated fermions: Hubbard and Falicov-Kimball models.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Exact results for strongly correlated fermions: Hubbard and Falicov-Kimball models./
作者:	Goldbaum, Pedro.
面頁冊數:	114 p.
附註:	Source: Dissertation Abstracts International, Volume: 66-03, Section: B, page: 1509.
Contained By:	Dissertation Abstracts International66-03B.
標題:	Physics, General. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3169799
ISBN:	054205955X

Exact results for strongly correlated fermions: Hubbard and Falicov-Kimball models.
Goldbaum, Pedro.

Exact results for strongly correlated fermions: Hubbard and Falicov-Kimball models. - 114 p.

Source: Dissertation Abstracts International, Volume: 66-03, Section: B, page: 1509.

Thesis (Ph.D.)--Princeton University, 2005.

In this work, we study two models of strongly correlated fermions: Hubbard and Falicov-Kimball. We present a proof of the existence of real and ordered solutions to the nested Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any U > 0 to U = infinity is also shown, where U is the strength of the interaction between fermions at the same site. We use this continuity property, combined with the proof that the norm of the wavefunction obtained with the generalized Bethe Ansatz is not zero, to prove that the solution gives us the ground state of the finite system, as assumed by Lieb and Wu. For the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the Lieb-Wu solution of the 1D Hubbard model.

ISBN: 054205955XSubjects--Topical Terms:

1018488
Physics, General.

Exact results for strongly correlated fermions: Hubbard and Falicov-Kimball models.
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245 1 0 $a Exact results for strongly correlated fermions: Hubbard and Falicov-Kimball models.
300 $a 114 p.
500 $a Source: Dissertation Abstracts International, Volume: 66-03, Section: B, page: 1509.
500 $a Adviser: Elliott Lieb.
502 $a Thesis (Ph.D.)--Princeton University, 2005.
520 $a In this work, we study two models of strongly correlated fermions: Hubbard and Falicov-Kimball. We present a proof of the existence of real and ordered solutions to the nested Bethe Ansatz equations for the one dimensional Hubbard model on a finite lattice, with periodic boundary conditions. The existence of a continuous set of solutions extending from any U > 0 to U = infinity is also shown, where U is the strength of the interaction between fermions at the same site. We use this continuity property, combined with the proof that the norm of the wavefunction obtained with the generalized Bethe Ansatz is not zero, to prove that the solution gives us the ground state of the finite system, as assumed by Lieb and Wu. For the absolute ground state at half-filling, we show that the solution converges to a distribution in the thermodynamic limit. This limit distribution satisfies the integral equations that led to the Lieb-Wu solution of the 1D Hubbard model.
520 $a We also obtain a lower bound for the ground state energy of the Falicov-Kimball model. This bound is given by a bulk term, plus a term proportional to the boundary. A numerical value for the coefficient of the boundary term is determined. The explicit derivation is important in the proof of the conjecture of segregation of the two kinds of fermions in the Falicov-Kimball model, for sufficiently large interactions.
590 $a School code: 0181.
650 4 $a Physics, General. $3 1018488
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710 2 0 $a Princeton University. $3 645579
773 0 $t Dissertation Abstracts International $g 66-03B.
790 1 0 $a Lieb, Elliott, $e advisor
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791 $a Ph.D.
792 $a 2005
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