Search

A hybrid theory which combines configuration interaction and Green's function approaches is proposed here to treat charged and neutral excitations. The theory is parameter free and reduces to the well-known Bethe-Salpeter equation (BSE) in the case of excitons. However, unlike the BSE, the theory can be applied to calculate any excitation beyond the exciton. As this type of computation is generally time consuming, we show that in the case of Wannier-type excitations, the localization in reciprocal space can be used to reduce the required computation load. We apply our approach to excitons and trions in ${\mathrm{WS}}_{2}$ and ${\mathrm{MoS}}_{2}$ transition metal dichalcogenides monolayers and obtain optical spectra, binding energies, and dark-bright exciton splitting in good agreement with experimental measurements. Moreover, in the case of ${\mathrm{WS}}_{2}$, we have found that the negative trion peak shows a fine structure splitting (FSS) of 15 meV which corresponds to the FSS for an isolated monolayer.

We report the results of our theoretical studies of the time-reversal and parity violating electric dipole moment (EDM) of $^{129}\mathrm{Xe}$ arising from the nuclear Schiff moment (NSM) and the electron-nucleus tensor-pseudotensor (T-PT) interaction based on the self-consistent and the normal relativistic coupled-cluster methods. The important many-body effects are highlighted and their contributions are explicitly presented. The uncertainties in the calculations of the correlation and relativistic effects are determined by estimating the contributions of the triples excitations and the Breit interaction, respectively, which together amount to about 0.7% for the NSM and 0.2% for the T-PT interactions. The results of our present work in combination with improved experimental limits for $^{129}\mathrm{Xe}$ EDM in the future would tighten the constraints on the hadronic $\mathcal{C}\mathcal{P}$ violating quantities, and this could provide important insights into new physics beyond the standard model of elementary particles.

The Ising model is a reference model for applications in quantum computing, and is often used as a benchmark for numerical simulations. Classical Monte Carlo (MC) simulations are carried out only for finite-size lattices, and the result is generalized to the infinite-size lattice by data collapse. Lattice gauge techniques are diagrammatic techniques, that already work in the thermodynamic limit, and in general simulate link variables using classical MC, and Fermions as determinants. This leads to the infamous sign problem. In order to solve it, one replaces link variables with a Bosonic field, but it may have zero convergence radius. Here, link variables are replaced by a Grassmannian field. An algorithm is thus constructed, that makes it possible to obtain an expansion of the susceptibility, through which the values for the critical temperature and critical index γ are evaluated, respectively, within 1.6% and 5.4% of their accepted values.

In this review article, we survey some of our results pertaining to the search for the electric dipole moment of the electron (eEDM), using heavy polar molecules. In particular, we focus on the relativistic coupled cluster method (RCCM) and its applications to eEDM searches in YbF, HgX (X = F, Cl, Br, and I), BaF, HgA (A = Li, Na, and K), and YbOH. Our results are presented in a systematic manner, by first introducing the eEDM and its measurement using molecules, the importance of relativistic many-body theory, and finally our results, followed by future prospects.

We consider a magnetic insulator in contact with a normal metal. We derive a self-consistent Keldysh effective action for the magnon gas that contains the effects of magnon-magnon interactions and contact with the metal to lowest order. Self-consistent expressions for the dispersion relation, temperature and chemical potential for magnons are derived. Based on this effective action, we study instabilities of the magnon gas that arise due to spin-current flowing across the interface between the normal metal and the magnetic insulator. We find that the stability phase diagram is modified by an interference between magnon-magnon interactions and interfacial magnon-electron coupling. These effects persist at low temperatures and for thin magnetic insulators., 10 pages and 5 figures

In this paper a resummed thermodynamic perturbation theory is developed which accounts for both positive and negative hydrogen bond cooperativity in water. The theory is developed in Wertheim's multi-density statistical mechanics. We demonstrate that the hydrogen bonded structure of water is controlled by positive hydrogen bond cooperativity in homodromic hydrogen bonded clusters. Inclusion of negative anti-cooperativity in antidromic hydrogen bonded structures has little effect on the underlying hydrogen bond structure of liquid water. The resummed perturbation theory is shown to give hydrogen bond statistics consistent with first principles ab initio molecular dynamics simulations. In addition, the theory is shown to be in good agreement with experiment in the prediction of the average number of hydrogen bonds per water molecule in a liquid at ambient conditions. Finally, we develop a full thermodynamic model for water by including contributions to the free energy for isotropic square well attractions. We demonstrate that the model gives good representation of saturated liquid density, hydrogen bonding and vapor pressure. In addition, we show the full model predicts the anomalous minima in isothermal compressibility and isobaric heat capacity.

Non-perturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with non-perturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons (2q$\otimes$2phonon), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of $^{42,48}$Ca and $^{68}$Ni nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors., Comment: Article: 28 pages, 19 figures

We advance the Coupled Cluster method’s in the time-dependent realm, by imple- menting a robust solver based on the orbital-adaptive time-dependent Coupled Cluster (OATDCC)[1] method. This involves implementing both a simplified static orbital time-dependent coupled cluster solver with single and double excitations (TDCCSD) and an orbital-adaptive scheme with double excitations (OATDCCD). To supplement the time-dependent methods we implement several ground state solvers based on the Lagrangian Coupled Cluster formulation, with single and double excitations, as well as a non-orthogonal orbital-optimised Coupled Cluster (NOCC) solver[2]. We construct several quantum dot basis sets with different potential functions in one- and two dimensions, including interactions with magnetic fields. What is more, we also implement an interface with popular quantum chemistry software modules PySCF[3] and Psi4[4] for extraction of additional basis sets for atoms and molecules. The quantum systems are allowed to vary with time by addition of a time-dependent term to the Hamiltonian, with which we simulate a laser field in the dipole approxima- tion. As a validation we reproduce results from the scientific literature, both for atoms, molecules and quantum dots. We show that our methods lead to convergence in the ever-increasing basis set size limit, for simple quantum dot systems. For the same quantum dot system, we show how sensitive a system is to changes in the frequency of a driving oscillating field. Frequencies closer to the resonant frequency lead to exctiations and increased energy. We are able to simulate systems that are fairly large - quantum dots in one- and two dimensions with up to twelve electrons. For systems that meander far from the reference state, we show that the orbital-adaptive method has far superior stability, compared with the method with static orbitals. For all quantum dot systems we find strong comformity with the harmonic potential theorem[5], yet we see a slight many-body effect for a two-dimensional double dot system. By subjecting the two-dimensional quantum dots to a homogoenous, static magnetic field in the form of an angular momentum operator, we see two frequencies in the dipole spectrum, instead of one frequency. This is also in accordance with the harmonic potential theorem. The difference between the two frequencies in the new spectrum is the same as the Larmor frequency of the magnetic field, within acceptable tolerance levels.

Solutions to the time-dependent Schrödinger equation are central to the understanding of the interaction between particles and external probes. The increasing availability of intense laser fields in experiments has spawned an interest in the study of the dynamics of many-body systems interacting with strong laser pulses. However, the complexity of the many-body problem quickly becomes a significant roadblock in the exploration of larger atoms and molecules, thus limiting the size of the systems that can be explored. Real-time ab initio electronic structure theory provides promising methods for investigating the dynamics of matter-field interactions and we have implemented several many-body methods which we use to analyze atoms and molecules subject to intense laser fields. We implement three different ab initio real-time methods: Hartree-Fock, configuration interaction, and coupled-cluster which we apply to systems of atoms and molecules. A thorough theory section outlines the foundation of our work. We demonstrate the strengths of the implemented methods and highlight the applicability of the orbital-adaptive time-dependent coupled-cluster method with doubles excitations by showcasing how this method is stable where the more conventional time-dependent coupled-cluster method with singles-and-doubles excitations fail. We demonstrate the first dipole allowed transition energy for Neon and Argon in the aug-cc-pVDZ basis to be 19.4327 eV and 12.7275 eV, respectively. Finally, we end this thesis demonstrating the versatility of our implemented methods by exhibiting simulations of exotic systems with spin-dependent laser fields and ionization of the one-dimensional Beryllium atom.

Quantum statistics is a many body theory describing macroscopic matter. Let us first summarize concepts of classical many body theory and subsequently concepts of many body quantum theory, just what we need in the following. After this we will proceed to the simplest quantum statistical ensembles.

Given elementary inter-nucleon interactions,the resolution of the A-body Schrödinger equation gives access to the properties of the nuclear eigenstates. Many-body perturbation theory (MBPT) based on a Hartree-Fock mean field allows one to treat the dynamical correlations at play in doubly-closed-shell nuclei. Beyond shell closures,breaking U(1) symmetry associated with the conservation of neutron and proton numbers further permits to capture static correlations at the meanfield level and to formulate the well-behaved Bogoliubov many-body perturbation theory (BMBPT).Nevertheless, BMBPT results show contaminations associated with the broken symmetry that is only emergent on finite quantum system such as theatomic nucleus. Thus, the restoration of U(1) symmetry beyond the mean field is necessary for acorrect description and gives rise to the projected BMBPT method (PBMBPT). The goal is to implement PBMBPT in order to perform ab initio calculations of singly-open-shell mid-mass nuclei.The present work provides systematic solutions to the formal and technical problems arising during the implementation of PBMBPT: an automatic and safe method to generate PBMBPT diagrams and associated expressions, a framework to calculate other observables than the energy, an extension of the normal ordering approximation to symmetry breaking methods as well as an automatic and safe tool for spherical reduction of tensor networks., Étant donnée l’interaction entre les nucléons,la résolution de l’équation de Schrödinger à A corps permet d’accéder aux propriétés des états quantiques des noyaux. La théorie des perturbations à N corps (MBPT) basée sur un état de champ moyen d’Hartree-Fock permet de traiter les corrélations dynamiques mises en jeu dans les noyaux à doubles couches fermées. Au-delà des fermetures de couches, la brisure spontanée de la symétrie U(1)associée à la conservation du nombre de protons et de neutrons permet en sus l’inclusion des corrélations statiques au niveau du champ moyen et la formulation de la théorie des perturbations à N corps de Bogoliubov (BMBPT). Néanmoins, les résultats des calculs BMBPT présentent des contaminations du fait que la brisure de symétrie n’est qu’émergente dans les systèmes quantiques finis tels que le noyau atomique. Ainsi, la restauration de la symétrie U(1) au-delà du champ moyen est nécessaire pour une description correcte et donne lieuà la formulation de la méthode BMBPT projetée(PBMBPT). Le but est d’implémenter PBMBPTafin d’effectuer des calculs ab initio pour les noyaux à couche ouverte et de masse intermédiaire. Le présent travail apporte des solutions systématiques aux problèmes formels et techniques qui se posent lorsde l’implémentation numérique de PBMBPT : une méthode automatique et sûre permettant de générer les diagrammes PBMBPT ainsi que les expressions correspondantes, un formalisme permettant de calculer d’autres observables que l’énergie, une extension de l’approximation en produit normal aux méthodes avec brisures de symétries ainsi qu’un outil automatique et sûr de réduction sphérique de réseaux de tenseurs.

In this article, we use a many-body approach to study the absorption spectra of electron-doped two-dimensional semiconductors. Optical absorption is modeled by a many-body scattering Hamiltonian which describes an exciton immersed in a Fermi sea. The interaction between electron and exciton is approximated by an effective scattering potential, and optical spectra are calculated by solving for the exciton Green's function. From this approach, a trion state can be assigned as a bound state of an electron-exciton scattering process, and the doping-dependent phenomena observed in the spectra can be attributed to several many-body effects induced by the interaction with the Fermi sea. While the many-body scattering Hamiltonian can not solved exactly, we reduce the problem to two limiting solvable situations. The first approach approximates the full many-body problem by a simple scattering process between the electron and the exciton, with a self-energy obtained by solving a Bethe-Salpeter equation (BSE). An alternate approach assumes an infinite mass for the exciton, such that the many-body scattering Hamiltonian reduces to a Mahan-Nozieres-De Dominicis (MND) model. The exciton Green's function can then be solved numerically exactly by a determinantal formulation, and the optical spectra show signatures of the Fermi-edge singularity at high doping densities. The full doping dependence and temperature dependence of the exciton and trion lineshapes are simulated via these two approximate approaches, with the results compared to each other and to experimental expectations., 17 pages, 4 figures

Respecting the conservation laws of momentum and energy in a many body theory is very important for understanding the transport phenomena. The previous conserving approximation requires that the self-energy of a single particle could be written as a functional derivative of a full dressed Green's function. This condition can not be satisfied in the G 0 G t-matrix or pair fluctuation theory which emphasizes the fermion pairing with a stronger than the Bardeen–Cooper–Schrieffer (BCS) attraction. In the previous work [1] , we have shown that when the temperature is above the superfluid transition temperature T c , the G 0 G t-matrix theory can be put into a form that satisfies the stress tensor Ward identity (WI) or local form of conservation laws by introducing a new type of vertex correction. In this paper, we will extend the above conservation approximation to the superfluid phase in the BCS mean field level. To establish the stress tensor WI, we have to include the fluctuation of the order parameter or the contribution from the Goldstone mode. The result will be useful for understanding the transport properties such as the behavior of the viscosity of Fermionic gases in the superfluid phases.

The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems.

The SternheimerGW software uses time-dependent density-functional perturbation theory to evaluate G W quasiparticle band structures and spectral functions for solids. Both the Green’s function G and the screened Coulomb interaction W are obtained by solving linear Sternheimer equations, thus overcoming the need for a summation over unoccupied states. The code targets the calculation of accurate spectral properties by convoluting G and W using a full frequency integration. The linear response approach allows users to evaluate the spectral function at arbitrary electron wavevectors, which is particularly useful for indirect band gap semiconductors and for simulations of angle-resolved photoelectron spectra. The software is parallelized efficiently, integrates with version 6.3 of Quantum Espresso, and is continuously monitored for stability using a test farm. Program summary Program Title: SternheimerGW Program Files doi: http://dx.doi.org/10.17632/7ywzjng9t5.1 Licensing provisions: GNU General Public License v3.0 Programming language: Fortran 2003 Nature of problem: The lack of the exchange–correlation discontinuity in density-functional theory (DFT) leads to a systematic underestimation of the band gap between conduction and valence states. Many-body perturbation theory in the G W approximation provides an effective solution to this problem, as well as other limitations faced by DFT in the description of electronic excitations. However, the G W method comes with its own set of limitations: (i) The perturbation of the system is typically expressed in terms of the unoccupied states, and achieving numerical convergence with respect to these states is often cumbersome. Since the underlying DFT codes rely only on the occupied states, their default behavior is often ill-suited to provide a sufficient amount of empty states. Combined with the large number of parameters that need to be converged, this limits the use of G W codes by non-expert users and automatic scripts. (ii) Currently, G W codes require that a homogeneous k -point mesh is used in the calculation. Hence, features close to the band edges are often only accessible via prohibitively expensive dense k -point meshes or interpolation techniques. (iii) To evaluate the frequency convolution of the Green’s function G and the screened Coulomb interaction W , many current G W calculations rely on approximations such as the plasmon-pole approximation, the analytic continuation, or the contour deformation. The relative merits and accuracy of the various approximations are not fully understood. Solution method: In SternheimerGW , we address (i) by replacing the summation over unoccupied states with a linear response equation. The solution depends on the occupied states only, and it employs linear response algorithms already provided by the Quantum ESPRESSO suite to compute phonons and related properties. As an additional benefit, transforming the problem in a linear response equation removes the restriction to homogeneous k -point meshes (ii), so that the G W self-energy for any arbitrary point can be evaluated. Finally (iii), we provide the possibility to perform a full frequency convolution along the real frequency axis. This feature can serve as a benchmark for approximate integrations using models or analytic continuation.

The last few decades in nuclear structure theory have seen a rapid expansion of ab initio theories, aiming at describing the properties of nuclei starting from the inter-nucleonic interaction. Such an expansion relied both on the tremendous growth of computing power and novel formal developments. This work focuses on the development of the recently proposed Bogoliubov Many-Body Perturbation Theory that relies on a particle-number-breaking reference state to tackle singly open-shell nuclei. The formalism is first described in details, and diagrammatic and algebraic contributions are derived up to second order. Its link to standard Many-Body Perturbation Theory is made explicit, as well as its connexion to Bogoliubov Coupled-Cluster theory. An automated extension to higher orders based on graph theory methods is then detailed, and the ADG numerical program generating and evaluating BMBPT diagrams at arbitrary order is introduced. Such a formal development carries implications that are not restricted to the present work, as the developed methods can be applied to other many-body methods. Finally, first numerical results obtained for oxygen, calcium and nickel isotopes are presented. They establish BMBPT as a method of interest for large-scale computations of isotopic or isotonic chains in the mid-mass sector of the nuclear chart., Les dernières décennies ont donné lieu à un développement rapide des théories ab initio visant à décrire les propriétés des noyaux à partir de l'interaction nucléonique. Un tel développement a été rendu possible à la fois par la très importante croissance de la puissance de calcul et de nouveaux développements formels. Le présent travail se consacre au développement de la théorie de perturbation à N corps de Bogolioubov récemment proposée, qui repose sur l'usage d'un état de référence brisant la symétrie associée au nombre de particules pour permettre une description des noyaux à simple couche ouverte. Le formalisme est tout d'abord décrit en détails, son lien avec la théorie de perturbation à N corps standard est établi, tout comme sa connexion avec la théorie de cluster couplés de Bogolioubov. L'extension du formalisme à des ordres plus élevés à partir de méthodes de théorie des graphes est ensuite présentée ainsi que le programme ADG qui génère et évalue les diagrammes BMBPT à un ordre quelconque. Les implications de ce développement formel dépassent le cadre du présent travail, les méthodes développées pouvant être appliqués à d’autres méthodes à N corps. Pour terminer, de premiers résultats numériques pour les isotopes de l'oxygène, du calcium et du nickel sont présentés. Ces résultats établissent la théorie de perturbation à N corps de Bogolioubov comme une méthode de premier intérêt pour des calculs à grande échelle sur les chaînes isotopiques et isotoniques de masse moyenne.

The Lipkin-Meshkov-Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schr\"odinger equation without making any approximation. The model, which in its unperturbed case is composed only by two energy levels, includes two interacting terms. A first one, the $V$ interaction, which promotes or degrade pairs of particles, and a second one, the $W$ interaction, which scatters one particle in the upper and another in the lower energy level. In comparing this model with other approximation methods, the $W$ term interaction is often set to zero. In this paper, we show how the presence of this interaction changes the global structure of the system, generates degeneracies between the various eigenstates and modifies the energy eigenvalues structure. We present analytical solutions for systems of two and three particles and, for some specific cases, also for four, six and eight particles. The solutions for systems with more than eight particles are only numerical but their behaviour can be well understood by considering the extrapolations of the analytical results. Of particular interest it is the study of how the $W$ interaction affects the energy gap between the ground state and the first-excited state., Comment: 17 pages, 8 figures

Unlike everyday applications on the ground, electronics in space are exposed to damaging radiation, and could misbehave unpredictably. This study employs atomistic molecular-dynamics simulations and many-body theory to analyze the effects of radiation-induced defects in semiconductors on the performance of satellite-borne optoelectronic devices. This technical approach, spanning initial material damage to final performance degradation, is important for space applications, as it allows the prediction of lifetime for space-based imaging technologies.

The problem of heat transport anisotropy in layered cuprate high temperature superconductors (HTS) has been investigated in terms of a−, b−, c− axis thermal conductivity. Various inadequacies involved due to dispersion and violation of Matthessien’s rule in the Callaway’s model have been removed with the help of life time approach of quantum many body theory of scattering mechanisms. Based on this approach the thermal conductivity of La1.98Sr0.02CuO4 and La1.96Sr0.04CuO4 samples has been numerically estimated and the observed results are found in good agreement with experimental observations.The problem of heat transport anisotropy in layered cuprate high temperature superconductors (HTS) has been investigated in terms of a−, b−, c− axis thermal conductivity. Various inadequacies involved due to dispersion and violation of Matthessien’s rule in the Callaway’s model have been removed with the help of life time approach of quantum many body theory of scattering mechanisms. Based on this approach the thermal conductivity of La1.98Sr0.02CuO4 and La1.96Sr0.04CuO4 samples has been numerically estimated and the observed results are found in good agreement with experimental observations.

Annihilation momentum densities and vertex enhancement factors for positron annihilation on valence and core electrons of noble-gas atoms are calculated using many-body theory for s, p and d-wave positrons of momenta up to the positronium-formation threshold. The enhancement factors parametrize the effects of short-range electron-positron correlations which increase the annihilation probability beyond the independent-particle approximation. For all positron partial waves and electron subshells, the enhancement factors are found to be relatively insensitive to the positron momentum. The enhancement factors for the core electron orbitals are also almost independent of the positron angular momentum. The largest enhancement factor (\({\sim }10\)) is found for the 5p orbital in Xe, while the values for the core orbitals are typically \({\sim }1.5\).

A novel Rayleigh-Schr\"odinger many-body perturbation theory (MBPT) approach is introduced by making use of a particle-number-breaking Bogoliubov reference state to tackle (near-)degenerate open-shell fermionic systems. By choosing a reference state that solves the Hartree-Fock-Bogoliubov variational problem, the approach reduces to the well-tested M{\o}ller-Plesset, i.e., Hartree-Fock based, MBPT when applied to closed-shell systems. Due to its algorithmic simplicity, the newly developed framework provides a computationally simple yet accurate alternative to state-of-the-art non-perturbative many-body approaches. At the price of working in the quasi-particle basis associated with a single-particle basis of sufficient size, the computational scaling of the method is independent of the particle number. This paper presents the first realistic applications of the method ranging from the oxygen to the nickel isotopic chains on the basis of a modern nuclear Hamiltonian derived from chiral effective field theory., Comment: 6 pages, 3 figures

This is a work extending the results of \cite{AH} and \cite{AHH}. We want to show convergence of the Schr\"odinger equation towards the Hartree equation with more natural assumptions. We first consider both the defocusing and the focusing semi-relativistic Hartree equation. We show that the tools of \cite{P} are essentially sufficient for deriving the Hartree equation in those cases. Next, we extend this result to the case of fractional Hartree equations with possibly more singular potentials than the Coulomb potential. Finally, we show that, in the non-relativistic case, one can derive the Hartree equation assuming only $L^2$-data in the case of potentials that are more than or as regular as the Coulomb potential. We also derive the Hartree equation for more singular potentials in this case. This work is inspired by talks given at the conference 'MCQM 2018' at Sapienza/Rome., Comment: 38 pages

Within the non-equilibrium Green's function (NEGF) formalism, the Generalized Kadanoff-Baym Ansatz (GKBA) has stood out as a computationally cheap method to investigate the dynamics of interacting quantum systems driven out of equilibrium. Current implementations of the NEGF--GKBA, however, suffer from a drawback: real-time simulations require {\em noncorrelated} states as initial states. Consequently, initial correlations must be built up through an adiabatic switching of the interaction before turning on any external field, a procedure that can be numerically highly expensive. In this work, we extend the NEGF--GKBA to allow for {\em correlated} states as initial states. Our scheme makes it possible to efficiently separate the calculation of the initial state from the real-time simulation, thus paving the way for enlarging the class of systems and external drivings accessible by the already successful NEGF--GKBA. We demonstrate the accuracy of the method and its improved performance in a model donor-acceptor dyad driven out of equilibrium by an external laser pulse.

The variational technique for nonequilibrium Green’s functions is derived resulting in the Hedin equations. This allows exploring of the high-density limit of diagrammatic expansions. Nonequilibrium Ward identities are presented. An asymmetric cummulant expansion of many-body Greens functions is developed resulting in asymmetric internal propagators which will become important for a consistent theory of pairing and condensation. All known approximations for the selfenergy are derived and reviewed with respect to asymmetric corrected propagators. The linear response formalism is discussed and the response for finite systems is presented. The link to functional renormalisation techniques is provided and integration of high-energy modes is discussed with hard and soft cut-off procedures.

Quantum-confined Stark effect (QCSE) of group IV Ge(Sn)/SiGe(Sn) quantum wells (QWs) on Si substrate is analyzed by microscopic many-body theory for mid-infrared (mid-IR) Si-based electroabsorption devices. To show the validity of the theory, QCSE of Ge/SiGe QW is investigated and very good agreement between theory and reported measured results is obtained. Next, the QCSE of GeSn/SiGeSn QWs is analyzed and the QW design for electroabsorption modulators to obtain large extinction ratio in mid-IR region is presented. It is shown that compressive and tensile strained well and barrier layers is preferable to obtain large extinction ratio due to its large conduction band offset.

Material gain of GeSn/SiGeSn quantum wells, which can be grown on Si substrate using a buffer layer, is analyzed based on microscopic many-body theory (MBT) for mid-infrared light sources based on Si photonics. MBT can consider a gain spectrum broadening associated with scattering phenomena, such as Coulomb scattering, based on quantum field theory, and does not need any artificial fitting parameters, such as a relaxation time, used in conventional analysis. Not only $\Gamma $ - but also carrier distributions in L-points are considered for the gain analysis. Using MBT, the quantum well structures maximizing the material gain and the differential gain at the threshold are investigated in terms of the well thickness, the strain, and the energy difference of quantum states between $\Gamma $ - and L-points.

In this paper, I give an overview of some selected results in quantum many body theory, lying at the interface between mathematical quantum statistical mechanics and condensed matter theory. In particular, I discuss some recent results on the universality of transport coefficients in lattice models of interacting electrons, with specific focus on the independence of the quantum Hall conductivity from the electron-electron interaction. In this context, the exchange of ideas between mathematical and theoretical physics proved particularly fruitful, and helped in clarifying the role played by quantum conservation laws (Ward Identities), together with the decay properties of the Euclidean current-current correlation functions, on the interaction-independence of the conductivity., 35 pages, 7 figures. These notes are based on a presentation given at the Istituto Lombardo, Accademia di Scienze e Lettere, in Milano (Italy) on May 5, 2016, as well as on the notes of a course given at the EMS-IAMP summer school in mathematical physics `Universality, Scaling Limits and Effective Theories', held in Roma (Italy) on July 11-15, 2016. Final version, accepted for publication

Which density functional is the ``best'' for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)---an accurate many body theory---is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite ${\mathrm{MAPbI}}_{3}$, a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approximate density functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the strongly constrained appropriately normed (SCAN) density functional yield very good agreement with the RPA. Finally, our study shows that in the room temperature tetragonal phase of ${\mathrm{MAPbI}}_{3}$, the molecules are preferentially parallel to the shorter lattice vectors but reorientation on ps time scales is still possible.

Material characteristics (optical gain/absorption, refractive index change) of GeSn/SiGeSn quantum wells in mid-IR region is theoretically investigated based on many-body theory. The strategies for designing quantum wells having large material gain or absorption under applied electric field are discussed.

We apply the pair interaction stability criteria of Fisher and Ruelle (1966 J. Math. Phys. 7 260) to establish the range of thermodynamic stability for a number of simple analytic potential forms used for condensed matter theory and modelling in the literature. We identify the ranges of potential parameters where, for a given potential, the system is thermodynamically stable, unstable and of uncertain stability. This was further explored by carrying out molecular dynamics simulations on the double Gaussian potential in the stable and unstable regimes. We show that, for example, the widely used exponential-6 and Born–Mayer–Huggins alkali halide potentials produce many-particle systems that are thermodynamically unstable.

We construct a many-body theory of magneto-elasticity in one dimension and show that the dynamical correlation functions of the quantum magnet, connecting the spins with phonons, involve all energy scales. Accounting for all magnetic states non-perturbatively via the exact diagonalisation techniques of Bethe ansatz, we find that the renormalisation of the phonon velocity is a non-monotonous function of the external magnetic field and identify a new mechanism for attenuation of phonons - via hybridisation with the continuum of excitations at high energy. We conduct ultrasonic measurements on a high-quality single crystal of the frustrated spin-1/2 Heisenberg antiferromagnet $\textrm{Cs}_{2}\textrm{CuCl}_{4}$ in its one-dimensional regime and confirm the theoretical predictions, demonstrating that ultrasound can be used as a powerful probe of strong correlations in one dimension., Comment: 17 pages, 9 figures