The adiabatic Holstein-Hubbard model describes electrons on a chain with step a interacting with themselves (with coupling U) and with a classical phonon field phi(x) (with coupling lambda). There is Peierls instability if the electronic ground-state energy F( p) as a functional of phi(x) has a minimum which corresponds to a periodic function with period pi/p(F), where p(F) is the Fermi momentum. We consider p(F)/pia irrational so that the charge-density wave is incommensurate with the chain. We prove in a rigorous way in the spinless case, when lambda, U are small and U/lambda large, that (a) when the electronic interaction is attractive U < 0 there is no Peierls instability and (b) when the interaction is repulsive U > 0 there is Peierls instability in the sense that our convergent expansion for F(phi), truncated at second order has a minimum which corresponds to an analytical and pi/p(F) periodic phi(x). Such a minimum is found solving an infinite set of coupled self-consistent equations, one for each of the infinite Fourier modes of phi(x).

Mastropietro, V. (2002). Incommensurate charge-density waves in the adiabatic Hubbard-Holstein model. PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS, 65(7), 751131-7511312 [10.1103/PhysRevB.65.075113].

Incommensurate charge-density waves in the adiabatic Hubbard-Holstein model

MASTROPIETRO, VIERI
2002-01-01

Abstract

The adiabatic Holstein-Hubbard model describes electrons on a chain with step a interacting with themselves (with coupling U) and with a classical phonon field phi(x) (with coupling lambda). There is Peierls instability if the electronic ground-state energy F( p) as a functional of phi(x) has a minimum which corresponds to a periodic function with period pi/p(F), where p(F) is the Fermi momentum. We consider p(F)/pia irrational so that the charge-density wave is incommensurate with the chain. We prove in a rigorous way in the spinless case, when lambda, U are small and U/lambda large, that (a) when the electronic interaction is attractive U < 0 there is no Peierls instability and (b) when the interaction is repulsive U > 0 there is Peierls instability in the sense that our convergent expansion for F(phi), truncated at second order has a minimum which corresponds to an analytical and pi/p(F) periodic phi(x). Such a minimum is found solving an infinite set of coupled self-consistent equations, one for each of the infinite Fourier modes of phi(x).
2002
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/07 - FISICA MATEMATICA
English
Con Impact Factor ISI
article; density; electron; Fourier analysis; mathematical model; molecular interaction; waveform
http://prb.aps.org/abstract/PRB/v65/i7/e075113
Mastropietro, V. (2002). Incommensurate charge-density waves in the adiabatic Hubbard-Holstein model. PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS, 65(7), 751131-7511312 [10.1103/PhysRevB.65.075113].
Mastropietro, V
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/43739
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