2015/03/31 by Adrian Stan, Pina Romaniello, Santiago Rigamonti +2 · 1 citation
Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Correlation #Physics #Quantum many-body systems #Quantum, superfluid, helium dynamics #Statistical physics #Theoretical physics #cond-mat.mtrl-sci
paper · pdf · doi:10.1088/1367-2630/17/9/093045
5 pages, 3 figures plus supplemental material
arxiv created 2015/04/21 · openalex publication_date 2015/09/25 · arxiv updated 2015/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.