TY - JOUR
T1 - Unphysical and physical solutions in many-body theories: from weak to strong correlation
JF - NEW JOURNAL OF PHYSICS
Y1 - 2015
A1 - Stan, Adrian
A1 - Romaniello, Pina
A1 - Rigamonti, Santiago
A1 - Reining, Lucia
A1 - Berger, JA
KW - dynamical mean-field theory
KW - many-body perturbation theory
KW - multiple solutions
KW - time-dependent density functional theory
AB - Many-body theory is largely based on self-consistent equations that are constructed in terms of the physical quantity of interest itself, for example the density. Therefore, the calculation of important properties such as total energies or photoemission spectra requires the solution of nonlinear equations that have unphysical and physical solutions. In this work we show in which circumstances one runs into an unphysical solution, and we indicate how one can overcome this problem. Moreover, we solve the puzzle of when and why the interacting Green's function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Green's function. Our results are general since they originate from the fundamental structure of the equations. The absorption spectrum of lithium fluoride is shown as one illustration, and observations in the literature for some widely used models are explained by our approach. Our findings apply to both the weak and strong-correlation regimes. For the strong-correlation regime we show that one cannot use the expressions that are obtained from standard perturbation theory, and we suggest a different approach that is exact in the limit of strong interaction.
PB - IOP PUBLISHING LTD
CY - TEMPLE CIRCUS, TEMPLE WAY, BRISTOL BS1 6BE, ENGLAND
VL - 17
ER -