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These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of…
A phenomenological theory is presented for two-dimensional quantum liquids in terms of the Fermi surface geometry. It is shown that there is a one-to-one correspondence between the properties of an interacting electron system and its…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
Quantum gravity has become a fertile interface between gravitational physics and quantum many-body physics, with its double goal of identifying the microscopic constituents of the universe and their fundamental dynamics, and of…
The methods of quantum chemistry and solid state theory to solve the many-body problem are reviewed. We start with the definitions of reduced density matrices, their properties (contraction sum rules, spectral resolutions, cumulant…
Since the pioneering work of L\"uscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While…
We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…
We discuss the possibility to modify many-body Hilbert quantum formalism that is necessary for the representation of quantum systems dynamics. The notion of effective classical algorithm and visualization of quantum dynamics play the key…
Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual…
Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to…
For over twenty years, ultra-cold atomic systems have formed an almost perfect arena for simulating different quantum many-body phenomena and exposing their non-obvious and very often counterintuitive features. Thanks to extremely precise…
Using the trajectory conception of state we give a simple demonstration that the quantum state of a many-body system may be expressed as a set of states in three-dimensional space, one associated with each particle. It follows that the…
The characterization of quantum critical phenomena is pivotal for the understanding and harnessing of quantum many-body physics. However, their complexity makes the inference of such fundamental processes difficult. Thus, efficient and…
We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported…
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…
While many studies point towards the existence of many-body localization (MBL) in one dimension, the fate of higher-dimensional strongly disordered systems is a topic of current debate. The latest experiments as well as several recent…
We summarise the recent theoretical progress in few-body descriptions of the piNN system. Previous descriptions, both three- and four-dimensional, are shown to possess serious theoretical inconsistencies. We illustrate how three-dimensional…
Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment…
Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space…
Ultracold atoms in optical lattices have proven to provide an extremely clean and controlled setting to explore quantum many-body phases of matter. Now, imaging of atoms in such lattice structures has reached the level of single-atom…