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The degrees of freedom that confer to strongly correlated systems their many intriguing properties also render them fairly intractable through typical perturbative treatments. For this reason, the mechanisms responsible for these…
In this article we discuss the accuracy of effective one-dimensional theories used to describe the behavior of ultracold atomic ensembles confined in quantum wires by a harmonic trap. We derive within a fully many-body approach the…
In quantum many-body problems, one of the main difficulties comes from the description of non-negligible interactions which require, at least in principle, an exponential amount of information. Recently, in the context of spin glasses and…
Calculating bounds of properties of many-body quantum systems is of paramount importance, since they guide our understanding of emergent quantum phenomena and complement the insights obtained from estimation methods. Recent semidefinite…
The effective independent-particle (mean-field) approximation of the Hubbard Hamiltonian is described in a many-body basis to develop a formal comparison with the exact diagonalization of the full Hubbard model, using small atomic chain as…
This thesis presents a set of studies on atomic systems where quantum effects are particularly relevant. These studies have been developed by applying a variety of tools from many-body physics. First of all, we have studied the prospects…
In recent years many-body perturbation theory encountered a renaissance in the field of ab initio nuclear structure theory. In various applications it was shown that perturbation theory, including novel flavors of it, constitutes a useful…
Studying the physics of quantum correlations has gained new interest after it has become possible to measure entanglement entropies of few body systems in experiments with ultracold atomic gases. Apart from investigating trapped atom…
In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master…
Understanding strongly correlated quantum many-body states is one of the most difficult challenges in modern physics. For example, there remain fundamental open questions on the phase diagram of the Hubbard model, which describes strongly…
We adopt a geometric perspective on Fock space to provide two complementary insights into the eigenstates in many-body-localized fermionic systems. On the one hand, individual many-bodylocalized eigenstates are well approximated by a Slater…
Since John Bell formulated his paramount inequality for a pair of spin-$1/2$ particles, quantum mechanics has been confronted with the postulates of local realism with various equivalent configurations. Current technology, with its advanced…
Quantum many-body systems may defy thermalization even without disorder. Intriguingly, non-ergodicity may be caused by a fragmentation of the many-body Hilbert-space into dynamically disconnected subspaces. The tilted one-dimensional…
Simulating quantum systems in a finite volume is a powerful theoretical tool to extract information about them. Real-world properties of the system are encoded in how its discrete energy levels change with the size of the volume. This…
We apply the general principles of effective field theories to the construction of effective interactions suitable for few- and many-body calculations in a no-core shell model framework. We calculate the spectrum of systems with three and…
The transition from a few-body system to a many-body system can result in new length scales, novel collective phenomena or even in a phase transition. Such a threshold behavior was shown for example in 4He droplets, where 4He turns into a…
Many-body forces are sometimes a relevant ingredient in various fields, such as atomic, nuclear or hadronic physics. Their precise structure is generally difficult to uncover. So, phenomenological effective forces are often used in…
To perform efficient many-body calculations in the framework of the exact diagonalization of the Hamiltonian one needs an appropriately tailored Fock basis built from the single-particle orbitals. The simplest way to compose the basis is to…
For N impenetrable particles in one dimension where only the nearest and next-to-nearest neighbours interact, we obtain the complete spectrum both on a line and on a circle. Further, we establish a mapping between these N-body problems and…
A common situation in quantum many-body physics is that the underlying theories are known but too complicated to solve efficiently. In such cases one usually builds simpler effective theories as low-energy or large-scale alternatives to the…