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Register a new userUnphysical and Physical Solutions in Many-Body Theories: from Weak to Strong Correlation
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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 non-linear 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 Greens function does not unambiguously determine the underlying system, given in terms of its potential, or non-interacting Greens 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.
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In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order $N$ and plugged into the Dyson equation, which is then solved for the propagator $G_N$. For two simple examples of fermionic models -- the Hubbard atom at half filling and its zero space-time dimensional simplified version -- we find that $G_N$ converges when $Ntoinfty$ to a limit $G_infty,$, which coincides with the exact physical propagator $G_{rm exact} ,$ at small enough coupling, while $G_infty eq G_{rm exact} ,$ at strong coupling. We also demonstrate that it is possible to discriminate between these two regimes thanks to a criterion which does not require the knowledge of $G_{rm exact} ,$, as proposed in [Rossi et al., PRB 93, 161102(R) (2016)].
Many aspects of many-body localization (MBL), including dynamic classification of MBL phases, remain elusive. Here, by performing real-space renormalization group (RSRG) analysis we propose that there are two distinct types of MBL phases: strong MBL induced by quasiperiodic (QP) potential and weak MBL induced by random potential. Strong and weak MBL phases can be distinguished by their different probability distributions of thermal inclusion and entanglement entropy: exponential decay in strong MBL phases but power-law decay in weak MBL. We further discuss underlying mechanisms as well as experimental implications of having two distinct types of MBL phases. Strong MBL induced by QP potential may provide a more robust and promising platform for quantum information storage and processing.
The phase stability and equilibria of carbon dioxide is investigated from 125 -- 325K and 1 -- 10,000 atm using extensive molecular dynamics (MD) simulations and the Two-Phase Thermodynamics (2PT) method. We devise a direct approach for calculating phase diagrams in general, by considering the separate chemical potentials of the isolated phase at specific points on the P-T diagram. The unique ability of 2PT to accurately and efficiently approximate the entropy and Gibbs energy of liquids thus allows for assignment of phase boundaries from relatively short ($mathrm{sim}$ 100ps) MD simulations. We validate our approach by calculating the critical properties of the flexible Elementary Physical Model 2 (FEPM2), showing good agreement with previous results. We show, however, that the incorrect description of the short-range Pauli force and the lack of molecular charge polarization leads to deviations from experiments at high pressures. We thus develop a many-body, fluctuating charge model for CO${}_{2}$, termed CO${}_{2}$-Fq, from high level quantum mechanics (QM) calculations, that accurately captures the condensed phase vibrational properties of the solid (including the Fermi resonance at 1378 cm${}^{-1}$) as well as the diffusional properties of the liquid, leading to overall excellent agreement with experiments over the entire phase diagram. This work provides an efficient computational approach for determining phase diagrams of arbitrary systems and underscore the critical role of QM charge reorganization physics in molecular phase stability.
In this work we explore the performance of a recently derived many-body effective energy theory for the calculation of photoemission spectra in the regime of strong electron correlation. We apply the theory to paramagnetic MnO, FeO, CoO, and NiO, which are typical examples of strongly correlated materials and, therefore, a challenge for standard theories. We show that our methods open a correlation gap in all the oxides studied without breaking the symmetry. Although the materials seem similar, we show that an analysis of the occupation numbers reveals that the nature of the gap is not the same for these materials. Overall the results are very promising, although improvements are clearly required, since the band gap is overestimated for all the systems studied. We indicate some possible strategies to further develop the theory.
We present a detailed study of the coupling-constant-averaged exchange-correlation hole density at a jellium surface, which we obtain in the random-phase approximation (RPA) of many-body theory. We report contour plots of the exchange-only and exchange-correlation hole densities, the integration of the exchange-correlation hole density over the surface plane, the on-top correlation hole, and the energy density. We find that the on-top correlation hole is accurately described by local and semilocal density-functional approximations. We also find that for electrons that are localized far outside the surface the main part of the corresponding exchange-correlation hole is localized at the image plane.
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