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The statistics of gap ratios between consecutive energy levels is a widely used tool, in particular in the context of many-body physics, to distinguish between chaotic and integrable systems, described respectively by Gaussian ensembles of…
We review our results for the dynamics of isolated many-body quantum systems described by one-dimensional spin-1/2 models. We explain how the evolution of these systems depends on the initial state and the strength of the perturbation that…
We show that a singlet of many multi-level quantum systems arises naturally as the ground state of a physically-motivated Hamiltonian. The Hamiltonian simply exchanges the states of nearest-neighbours in some network of qudits (d-level…
We revisit qubit-qutrit quantum systems under collective dephasing and answer some of the questions which have not been asked and addressed so far in the literature. In particular, we examine the possibilities of non-trivial phenomena of…
We consider statistical methods based on finite samples of locally randomized measurements in order to certify different degrees of multiparticle entanglement in intermediate-scale quantum systems. We first introduce hierarchies of…
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…
We investigate the phenomenon of Hilbert space fragmentation (HSF) in open quantum systems and find that it can stabilize highly entangled steady states. For concreteness, we consider the Temperley-Lieb model, which exhibits quantum HSF in…
Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. Owing to the intimate…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
We consider a non-interacting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model) - a generic model of single-particle quantum chaos. We study the corresponding…
We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the…
We implement an algorithm which is aimed to reduce the dimensions of the Hilbert space of quantum many-body systems by means of a renormalization procedure. We test the role and importance of different representations on the reduction…
The origin of continuous energy spectra in large disordered interacting quantum systems is one of the key unsolved problems in quantum physics. While small quantum systems with discrete energy levels are noiseless and stay coherent forever…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
As recently manifested , the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
We derive upper bounds for Hilbert-Schmidt's quantum coherence of general states of a $d$-level quantum system, a qudit, in terms of its incoherent uncertainty, with the latter quantified using the linear and von Neumann's entropies of the…
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state…
We review recent results on the dynamics of continuous collapse models (or equivalently continuous measurement models) on finite dimensional Hilbert spaces. We mainly study the pure collapse dynamics, and the competition between collapse…