In this paper we formulate a nonlocal density functional theory of inhomogeneous water. We model a water molecule as a couple of oppositely charged sites. The negatively charged sites interact with each other through the Lennard–Jones potential (steric and dispersion interactions), square-well potential (short-range specific interactions due to electron charge transfer), and Coulomb potential, whereas the positively charged sites interact with all types of sites by applying the Coulomb potential only. Taking into account the nonlocal packing effects via the fundamental measure theory, dispersion and specific interactions in the mean-field approximation, and electrostatic interactions at the many-body level through the random phase approximation, we describe the liquid–vapour interface. We demonstrate that our model without explicit account of the association of water molecules due to hydrogen bonding and with explicit account of the electrostatic interactions at the many-body level is able to describe the liquid–vapour coexistence curve and the surface tension at the ambient pressures and temperatures. We obtain very good agreement with available in the literature MD simulation results for density profile of liquid–vapour interface at ambient state parameters. The formulated theory can be used as a theoretical background for describing of the capillary phenomena, occurring in micro- and mesoporous materials.

Frustrated magnets realize exotic forms of quantum matter beyond conventional order. Due to a lack of controlled and unbiased methods to study frustration in three dimensions, many questions remain unanswered. While most established numerical techniques have limited applicability, approaches based on cluster expansions are promising alternatives. By design, they do not suffer from dimensionality or frustration and generate reliable insights into the thermodynamic limit without any restriction in the parameter space. This thesis makes significant methodological progress in controlled numerical approaches tailored to study frustration in three dimensions. It covers (i) an automatic detection algorithm for symmetries in generic clusters, (ii) a general approach to the numerical linked cluster algorithm to study finite - and zero - temperature properties, and (iii) an expansion method based on the linked cluster theorem to obtain a suitable dressing for valence-bond crystals. In particular, we study one of the archetypal problems of frustrated magnetism in three dimensions: the pyrochlore Heisenberg antiferromagnet. For the first time, we are able to unbiasedly resolve its thermodynamic quantities to a temperature far beyond the scale on which the Schottky anomaly occurs. The broad applicability of the numerical linked cluster algorithm allows for the systematic investigation of different spin-liquid candidate materials such as the Cerium-based pyrochlores Ce₂Zr₂O₇ and Ce₂Sn₂O₇. Despite a similar chemical composition, the algorithm finds fundamental differences in their quantum mechanical nature by constraining their microscopic exchange parameters. Zero temperature properties are even less accessible: Neither the nature of the ground state nor an estimate of its energy are known for the pyrochlore antiferromagnet. Large-scale density matrix renormalization group calculations pushed to three dimensions provide the first reliable estimate of its ground-state energy and yield robust evidence for a spontaneous inversion symmetry breaking manifesting itself as an energy density difference on the tetrahedral sublattice. The symmetry-breaking tendency of the model is further observed in the presence of an external magnetic field where similar calculations suggest a stable 1/2-magnetization plateau. Continuing the investigation of low-energy states, we propose a new family - exponentially numerous in the linear system size - of valence-bond crystals as potential ground states. Understanding the stability of the previously overlooked family of states suggests a remarkable change of perspective on frustration with a focus on unfrustrated motifs. In sum, these discoveries present significant progress towards resolving long-standing questions regarding the nature of the ground state of the quantum pyrochlore S=1/2 antiferromagnet. / Frustrierte Magnete realisieren exotische Formen von Quantenmaterie, welche gewöhnliche Ordnungen übersteigen. Viele etablierte numerische Methoden versagen bei Frustration in drei Dimensionen, da sie entweder nicht anwendbar sind, unkontrolliert sind oder bestimmte Zustände vorziehen. Clusteralgorithmen bilden eine vielversprechende Alternative. Sie erfahren keine Einschränkung durch die Dimensionalität oder die Frustration des Problems und erlauben daher zuverlässige Einblicke in den thermodynamischen Limes. Diese Arbeit präsentiert methodische Fortschritte von kontrollierbaren Ansätzen, welche auf frustrierte Systeme in drei Dimensionen zugeschnitten sind. Sie beinhaltet (i) die Entwicklung eines Algorithmus zur automatischen Detektion räumlicher Symmetrien für allgemeine Cluster, (ii) einen allgemeinen Zugang zum 'numerical linked cluster algorithm'', um Eigenschaften bei endlicher Temperatur und dem absoluten Nullpunkt zu studieren und (iii) einen Clusteralgorithmus zur Optimierung des Zustands eines 'valence-bond' Kristalls. Die methodischen Fortschritte dieser Arbeit tragen zur Lösung eines archetypischen Problems von frustriertem Magnetismus in drei Dimensionen bei: dem Pyrochlor Heisenberg Antiferromagnet. Sie erlauben zuverlässige Einblicke in die Thermodynamik bis hin zu nicht-trivialen Temperaturen weit unter der Schottky-Anomalie. Die weiten Anwendungsmöglichkeiten des Clusteralgorithmus macht die systematische Untersuchung von Spinflüssigkeitskandidaten, wie die auf Cer basierenden Pyrochlore Ce₂Zr₂O₇ und Ce₂Sn₂O₇, möglich. Trotz einer ähnlichen chemischen Komposition, findet der Algorithmus fundamentale Unterschiede in ihrer quantenmechanischen Struktur. Frustration in drei Dimensionen ist am absoluten Nullpunkt ähnlich unzugänglich wie bei endlicher Temperatur und weder der Grundzustand, noch Schätzungen der Grundzustandsenergie des Pyrochlor Antiferromagneten sind bekannt. Groß angelegte Dichtematrixrenomierungsgruppenrechnungen in drei Dimensionen ermöglichen erstmals eine verlässliche Schätzung der Energie und finden eine spontan gebrochene Inversionssymmetrie, welche durch einen Unterschied in der Energiedichte auf dem tetraedrischen Untergitter ausgedrückt ist. Die Tendenz, die Symmetrie des Systems zu brechen, ist auch in der Präsenz eines externen magnetischen Feldes zu beobachten. Rechnungen deuten die Stabilität des 1/2-Magnetisierungsplateaus an. Einen signifikanten Beitrag zum Verständnis des Heisenberg-Models auf dem Pyrochlor wird durch eine Familie von potentiellen Grundzuständen geleistet, welche als harte Hexagone im Gitter visualisiert werden können. Ihre Anzahl skaliert exponentiell in der linearen Systemgröße und ihre niedrige Energie eröffnet eine neue Sichtweise auf frustrierte Magnete, welche den Fokus auf unfrustrierte Geometrien lenkt. Im Widerspruch zu der prominenten Spinflüssigkeitsannahme deuten die Ergebnisse dieser Arbeit auf Ordnung im Pyrochlor Antiferromagneten hin.

This thesis explores systems that exhibit strong coupling between an optical cavity field and a many-particle system. To treat the drive and dissipative nature of the cavity on the same footing as the dynamics of the many-particle system, we use a non-equilibrium field theoretic approach. The first system considered is an ultracold bosonic gas trapped inside a cavity. The dispersive coupling between the cavity field and the atoms' motion leads to the formation of a polariton. We show how a modulation of the pump laser on the energy scale of the transverse cavity mode splitting can be used to create effective interactions between different cavity modes. This effective interaction results in the polariton acquiring a multimode nature, exemplified by avoided crossings in the cavity spectrum. As the laser power is increased, the polariton softens and at a critical power becomes unstable. This instability signals the transition into a superradiant state. If the multimode polariton contains a cavity mode with an effective negative detuning, then the transition does not happen through a mode softening but at a finite frequency. To investigate this, classical non-linear equations are constructed from the action and from these we derive the critical couplings and frequencies. It is shown how the superradiant transition happening at a finite frequency is a consequence of a competition between the negatively and the positively detuned cavity modes making up the polariton. The finite-frequency transition is found to be equivalent to a Hopf bifurcation and leads to the emergence of limit cycles. Our analysis shows that the system can exhibit both bistabilities and evolution constricted to a two-torus. We end the investigation by showing how interactions among the atoms combined with the emerging limit cycle open new phonon scattering channels. The second system considered in the thesis is inspired by the recent experiments on gated Transition-metal dichalcogenides (TMD) monolayers inside cavities. An exciton within the TMD can couple strongly to the cavity and, due to the electronic gating, also interact strongly with the conduction electrons. To treat the strong interactions of the excitons with both cavity and electrons, we solve the coupled equations for the correlation functions non-perturbatively within a ladder approximation. The strong interactions give rise to new quasiparticles known as polaron-polaritons. By driving the system through the cavity, we show how the competition between electron-induced momentum relaxation and cavity loss leads to the accumulation of polaritons at a small but finite momentum, which is accompanied by significant decrease of the polariton linewidth Due to the hybrid nature of the polaron-polariton, we show that this behavior can by qualitatively modified by changing the cavity detuning.

Entanglement is a fundamental property of quantum systems and its characterization is a central problem for physics. Moreover, there is an increasing demand for scalable protocols that can certify the presence of entanglement. This is primarily due to the role of entanglement as a crucial resource for quantum technologies. However, systematic entanglement certification is highly challenging, and this is particularly the case for quantum many-body systems. In this dissertation, we tackle this challenge and introduce some techniques that allow the certification of multipartite entanglement in many-body systems. This is demonstrated with an application to a model of interacting fermions that shows the presence of resilient multipartite entanglement at finite temperatures. Moreover, we also discuss some subtleties concerning the definition entanglement in systems of indistinguishable particles and provide a formal characterization of multipartite mode entanglement. This requires us to work with an abstract formalism that can be used to define entanglement in quantum many-body systems without reference to a specific structure of the states. To further showcase this technique, and also motivated by current quantum simulation efforts, we use it to extend the framework of entanglement witnesses to lattice gauge theories. / L'entanglement è una proprietà fondamentale dei sistemi quantistici e la sua caratterizzazione è un problema centrale per la fisica. Inoltre, vi è una crescente richiesta di protocolli scalabili in grado di certificare la presenza di entanglement. Ciò è dovuto principalmente al ruolo dell'entanglement come risorsa cruciale per le tecnologie quantistiche. Tuttavia, la certificazione sistematica dell'entanglement è molto impegnativa, e questo è particolarmente vero per i sistemi quantistici a molti corpi. In questa dissertazione, affrontiamo questa sfida e introduciamo alcune tecniche che consentono la certificazione dell'entanglement multipartito in sistemi a molti corpi. Ciò è dimostrato con un'applicazione a un modello di fermioni interagenti che mostra la presenza di entanglement multipartito resiliente a temperature finite. Inoltre, discutiamo anche alcune sottigliezze riguardanti la definizione di entanglement in sistemi di particelle indistinguibili e forniamo una caratterizzazione formale dell'entanglement multipartito. Ciò ci richiede di lavorare con un formalismo astratto che può essere utilizzato per definire l'entanglement nei sistemi quantistici a molti corpi senza fare riferimento a una struttura specifica degli stati. Per mostrare ulteriormente questa tecnica, e anche motivata dagli attuali sforzi di simulazione quantistica, la usiamo per estendere la struttura dei testimoni di entanglement alle teorie di gauge del reticolo.

Nuclei are objects made of nucleons, protons and neutrons. Several dynamical processes that occur in nuclei are of great interest for the scientific community and for possible applications. For example, nuclear fusion can help us produce a large amount of energy with a limited use of resources and environmental impact. Few-nucleon scattering is an essential ingredient to understand and describe the physics of the core of a star. The classical computational algorithms that aim to simulate microscopic quantum systems suffer from the exponential growth of the computational time when the number of particles is increased. Even using today's most powerful HPC devices, the simulation of many processes, such as the nuclear scattering and fusion, is out of reach due to the excessive amount of computational time needed. In the 1980s, Feynman suggested that quantum computers might be more efficient than classical devices in simulating many-particle quantum systems. Following Feynman's idea of quantum computing, a complete change in the computation devices and in the simulation protocols has been explored in the recent years, moving towards quantum computations. Recently, the perspective of a realistic implementation of efficient quantum calculations was proved both experimentally and theoretically. Nevertheless, we are not in an era of fully functional quantum devices yet, but rather in the so-called "Noisy Intermediate-Scale Quantum" (NISQ) era. As of today, quantum simulations still suffer from the limitations of imperfect gate implementations and the quantum noise of the machine that impair the performance of the device. In this NISQ era, studies of complex nuclear systems are out of reach. The evolution and improvement of quantum devices will hopefully help us solve hard quantum problems in the coming years. At present quantum machines can be used to produce demonstrations or, at best, preliminary studies of the dynamics of a few nucleons systems (or other equivalent simple quantum systems). These systems are to be considered mostly toy models for developing prospective quantum algorithms. However, in the future, these algorithms may become efficient enough to allow simulating complex quantum systems in a quantum device, proving more efficient than classical devices, and eventually helping us study hard quantum systems. This is the main goal of this work, developing quantum algorithms, potentially useful in studying the quantum many body problem, and attempting to implement such quantum algorithms in different, existing quantum devices. In particular, the simulations made use of the IBM QPU's , of the Advanced Quantum Testbed (AQT) at Lawrence Berkeley National Laboratory (LBNL), and of the quantum testbed recently based at Lawrence Livermore National Laboratory (LLNL) (or using a device-level simulator of this machine). The our research aims are to develop quantum algorithms for general quantum processors. Therefore, the same developed quantum algorithms are implemented in different quantum processors to test their efficiency. Moreover, some uses of quantum processors are also conditioned by their availability during the time span of my PhD. The most common way to implement some quantum algorithms is to combine a discrete set of so-called elementary gates. A quantum operation is then realized in term of a sequence of such gates. This approach suffers from the large number of gates (depth of a quantum circuit) generally needed to describe the dynamics of a complex system. An excessively large circuit depth is problematic, since the presence of quantum noise would effectively erase all the information during the simulation. It is still possible to use error-correction techniques, but they require a huge amount of extra quantum register (ancilla qubits). An alternative technique that can be used to address these problems is the so-called "optimal control technique". Specifically, rather than employing a set of pre-packaged quantum gates, it is possible to optimize the external physical drive (for example, a suitably modulated electromagnetic pulse) that encodes a multi-level complex quantum gate. In this thesis, we start from the work of Holland et al. "Optimal control for the quantum simulation of nuclear dynamics" Physical Review A 101.6 (2020): 062307, where a quantum simulation of real-time neutron-neutron dynamics is proposed, in which the propagation of the system is enacted by a single dense multi-level gate derived from the nuclear spin-interaction at leading order (LO) of chiral effective field theory (EFT) through an optimal control technique. Hence, we will generalize the two neutron spin simulations, re-including spatial degrees of freedom with a hybrid algorithm. The spin dynamics are implemented within the quantum processor and the spatial dynamics are computed applying classical algorithms. We called this method classical-quantum coprocessing. The quantum simulations using optimized optimal control methods and discrete get set approach will be presented. By applying the coprocessing scheme through the optimal control, we have a possible bottleneck due to the requested classical computational time to compute the microwave pulses. A solution to this problem will be presented. Furthermore, an investigation of an improved way to efficiently compile quantum circuits based on the Similarity Renormalization Group will be discussed. This method simplifies the compilation in terms of digital gates. The most important result contained in this thesis is the development of an algorithm for performing an imaginary time propagation on a quantum chip. It belongs to the class of methods for evaluating the ground state of a quantum system, based on operating a Wick rotation of the real time evolution operator. The resulting propagator is not unitary, implementing in some way a dissipation mechanism that naturally leads the system towards its lowest energy state. Evolution in imaginary time is a well-known technique for finding the ground state of quantum many-body systems. It is at the heart of several numerical methods, including Quantum Monte Carlo techniques, that have been used with great success in quantum chemistry, condensed matter and nuclear physics. The classical implementations of imaginary time propagation suffer (with few exceptions) of an exponential increase in the computational cost with the dimension of the system. This fact calls for a generalization of the algorithm to quantum computers. The proposed algorithm is implemented by expanding the Hilbert space of the system under investigation by means of ancillary qubits. The projection is obtained by applying a series of unitary transformations having the effect of dissipating the components of the initial state along excited states of the Hamiltonian into the ancillary space. A measurement of the ancillary qubit(s) will then remove such components, effectively implementing a "cooling" of the system. The theory and testing of this method, along with some proposals for improvements will be thoroughly discussed in the dedicated chapter.

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No description available.

Quantum many-body phenomena have been a focal point of the physics community for the last several decades. From material science and chemistry to model systems and quantum computing, diverse problems share mathematical description and challenges. A key roadblock in many subfields is the exponential increase in problem size with increasing number of quantum constituents. Therefore, development of efficient compression and approximation methods is the only way to move forward. Parameterized models coming from the field of machine learning have successfully been applied to very large classical problems where data is abundant, leveraging recent advances in high-performance computing. In this thesis, state-of-the-art methods relying on such models are applied to the quantum many-body problem in two distinct ways: from first principles and data-driven, as described in chapter 1. In chapters 2 and 3, the framework of quantum Monte Carlo is used to efficiently manipulate variational approximations of many-body states, obtaining non-equilibrium states occurring in quantum circuits and real-time dynamics of large systems. In chapters 4 and 5, simulated synthetic data is used to train surrogate models that enhance original methods, allowing for computations that would otherwise be out of reach for conventional solvers. In all cases, a computational advantage is established when using machine learning methods to compress different versions of the quantum many-body problem. Each chapter is concluded by proposing extensions and novel applications of new compressed representation of the problem.

We study the low-temperature physics arising in models of a strongly correlated, tunnel-coupled double quantum dot (DQD), particularly the two-impurity Anderson model (2AIM) and the two-impurity Kondo model (2IKM), employing a combination of physical arguments and the Numerical Renormalisation Group. These models exhibit a rich range of Kondo physics. In the regime with essentially one electron on each dot, there is a competition between the Kondo effect and the interdot exchange interaction. This competition gives rise to a quantum phase transition (QPT) between local singlet and Kondo singlet phases in the 2IKM, which becomes a continuous crossover in the 2AIM as a result of the interlead charge transfer present. The 2IKM is known to exhibit two-channel Kondo (2CK) physics at the QPT, and we investigate whether this is also the case for the 2AIM at the crossover. We find that while in principle 2CK physics can be observed in the 2AIM, extremely low temperatures are required, such that it is unlikely that 2CK physics will be observed in an experimental DQD system in the near future. We have studied the effect of a magnetic field on the 2AIM and the 2IKM, finding that both the zero-field QPT in the 2IKM and the zero-field crossover in the 2AIM, persist to finite field. This presents the possibility of observing 2CK physics in an experimental DQD at finite field, but we find that the temperatures required to do so are extremely low. We show that longer even-numbered chains of spins also exhibit QPTs at finite field, and argue that a 2N-spin chain should undergo N QPTs as field is increased (starting deep in the local singlet phase at zero field). We have also carried out a joint theoretical-experimental study of a carbon nanotube based DQD, in collaboration with Dr. Mark Buitelaar et al. The agreement between experimental and theoretical results is good, and the experiments are able to access the crossover present in the 2AIM at finite field. Furthermore, the experiments show the wide range of physics exhibited by DQD systems, and illustrate the utility of such systems in probing correlated electron physics.

<p>Atomic physics plays an important role in determining the evolution stages in a wide range of laboratory and cosmic plasmas. Therefore, the main contribution to our ability to model, infer and control plasma sources is the knowledge of underlying atomic processes. Of particular importance are reliable low temperature dielectronic recombination (DR) rate coefficients.</p><p>This thesis provides systematically calculated DR rate coefficients of lithium-like beryllium and sodium ions via ∆n = 0 doubly excited resonant states. The calculations are based on complex-scaled relativistic many-body perturbation theory in an all-order formulation within the single- and double-excitation coupled-cluster scheme, including radiative corrections.</p><p>Comparison of DR resonance parameters (energy levels, autoionization widths, radiative transition probabilities and strengths) between our theoretical predictions and the heavy-ion storage rings experiments (CRYRING-Stockholm and TSRHeidelberg) shows good agreement.</p><p>The intruder state problem is a principal obstacle for general application of the coupled-cluster formalism on doubly excited states. Thus, we have developed a technique designed to avoid the intruder state problem. It is based on a convenient partitioning of the Hilbert space and reformulation of the conventional set of pairequations. The general aspects of this development are discussed, and the effectiveness of its numerical implementation (within the non-relativistic framework) is selectively illustrated on autoionizing doubly excited states of helium.</p>