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Register a new userZero-temperature limit and statistical quasiparticles in many-body perturbation theory
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Added by
Corbinian Wellenhofer
Publication date
2018
fields
Physics
and research's language is
English
Authors
Corbinian Wellenhofer
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The order-by-order renormalization of the self-consistent mean-field potential in many-body perturbation theory for normal Fermi systems is investigated in detail. Building on previous work mainly by Balian and de Dominicis, as a key result we derive a thermodynamic perturbation series that manifests the consistency of the adiabatic zero-temperature formalism with perturbative statistical mechanics---for both isotropic and anisotropic systems---and satisfies at each order and for all temperatures the thermodynamic relations associated with Fermiliquid theory. These properties are proved to all orders.
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We describe the second version (v2.0.0) of the code ADG that automatically (1) generates all valid off-diagonal Bogoliubov many-body perturbation theory diagrams at play in particle-number projected Bogoliubov many-body perturbation theory (PNP-BMBPT) and (2) evaluates their algebraic expression to be implemented for numerical applications. This is achieved at any perturbative order $p$ for a Hamiltonian containing both two-body (four-legs) and three-body (six-legs) interactions (vertices). All valid off-diagonal BMBPT diagrams of order $p$ are systematically generated from the set of diagonal, i.e., unprojected, BMBPT diagrams. The production of the latter were described at length in https://doi.org/10.1016/j.cpc.2018.11.023 dealing with the first version of ADG. The automated evaluation of off-diagonal BMBPT diagrams relies both on the application of algebraic Feynmans rules and on the identification of a powerful diagrammatic rule providing the result of the remaining $p$-tuple time integral. The new diagrammatic rule generalizes the one already identified in https://doi.org/10.1016/j.cpc.2018.11.023 to evaluate diagonal BMBPT diagrams independently of their perturbative order and topology. The code ADG is written in Python3 and uses the graph manipulation package NetworkX. The code is kept flexible enough to be further expanded throughout the years to tackle the diagrammatics at play in various many-body formalisms that already exist or are yet to be formulated.
We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree-Fock solution to construct the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation in not feasible, we perform third-order calculation and compare to advanced ab initio coupled-cluster calculations for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into tin isotopic chain that are in excellent agreement with the best available coupled-cluster results at a fraction of the computational cost.
The computation of the thermodynamic properties of nuclear matter is a central task of theoretical nuclear physics. The nuclear equation of state is an essential quantity in nuclear astrophysics and governs the properties of neutron stars and core-collapse supernovae. The framework of chiral effective field theory provides the basis for the description of nuclear interactions in terms of a systematic low-energy expansion. In this thesis, we apply chiral two- and three-nucleon interactions in perturbative many-body calculations of the thermodynamic equation of state of infinite homogeneous nuclear matter. The conceptual issues that arise concerning the consistent generalization of the standard zero-temperature form of many-body perturbation theory to finite temperatures are investigated in detail. The structure of many-body perturbation theory at higher orders is examined, in particular concerning the role of the so-called anomalous contributions. The first-order nuclear liquid-gas phase transition is analyzed with respect to its dependence on temperature and the neutron-to-proton ratio. Furthermore, the convergence behavior of the expansion of the equation of state in terms of the isospin asymmetry is examined. It is shown that the expansion coefficients beyond the quadratic order diverge in the zero-temperature limit, implying a nonanalytic form of the isospin-asymmetry dependence at low temperatures. This behavior is associated with logarithmic terms in the isospin-asymmetry dependence at zero temperature.
Recently, the zero-pairing limit of Hartree-Fock-Bogoliubov (HFB) mean-field theory was studied in detail in arXiv:2006.02871. It was shown that such a limit is always well-defined for any particle number A, but the resulting many-body description differs qualitatively depending on whether the system is of closed-(sub)shell or open-(sub)shell nature. Here, we extend the discussion to the more general framework of Finite-Temperature HFB (FTHFB) which deals with statistical density operators, instead of pure many-body states. We scrutinize in detail the zero-temperature and zero-pairing limits of such a description, and in particular the combination of both limits. For closed-shell systems, we find that the FTHFB formulism reduces to the (zero-temperature) Hartree-Fock formulism, i.e. we recover the textbook solution. For open-shell systems, however, the resulting description depends on the order in which both limits are taken: if the zero-temperature limit is performed first, the FTHFB density operator demotes to a pure state which is a linear combination of a finite number of Slater determinants, i.e. the case of arXiv:2006.02871. If the zero-pairing limit is performed first, the FTHFB density operator remains a mixture of a finite number of Slater determinants with non-zero entropy, even as the temperature vanishes. These analytical findings are illustrated numerically for a series of Oxygen isotopes.
We numerically study both the avalanche instability and many-body resonances in strongly-disordered spin chains exhibiting many-body localization (MBL). We distinguish between a finite-size/time MBL regime, and the asymptotic MBL phase, and identify some landmarks within the MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in infinite-length systems, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide resonances. We find that the effective matrix elements producing eigenstates with system-wide resonances are enormously broadly distributed. This means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime in to three subregimes: (i) at strongest disorder, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not; and (iii) in the weaker randomness regime, the minimum gap is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i).
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