Related papers: An application of renormalization in Hilbert space…
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large…
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By…
The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and…
By means of a diagram technique for Hubbard operators we show the existence of a spin-dependent renormalization of the localized levels in an interacting region, e.g. quantum dot, modeled by the Anderson Hamiltonian with two conduction…
We introduce novel characterizations for many-body phase transitions between delocalized and localized phases based on the system's sensitivity to boundary conditions. In particular, we change boundary conditions from periodic to…
The obstruction to constructing localized degrees of freedom is a signature of several interesting condensed matter phases. We introduce a localization renormalization procedure that harnesses this property, and apply our method to…
Quantum thermalization occurs in a broad class of systems from elementary particles to complex materials. Out-of-equilibrium quantum systems have long been understood to either thermalize or retain memory of their initial states, but not…
Multi-component quantum systems in strong interaction with their environment are receiving increasing attention due to their importance in a variety of contexts, ranging from solid state quantum information processing to the quantum…
Global changes of states are of crucial importance in optimization algorithms. We review some heuristic algorithms in which global updates are realized by a sort of real-space renormalization group transformation. Emphasis is on the…
We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are…
Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply…
Quantum probes that enable enhanced exploration and characterization of complex systems are central to modern science, spanning applications from biology to astrophysics and chemical design. In large many-body quantum systems, interactions…
In this thesis, I go through the well-known solutions to the one and two-particle systems trapped in a quantum harmonic oscillator and then continue to the three, four and many-body quantum systems. This is done by developing new analytical…
Stabilizing thermodynamically unstable phases in many-body systems, such as suppressing pathological neuronal synchronization in Parkinson's disease or maintaining magnetic order across broad temperature ranges, remains a persistent…
A method is proposed to improve the accuracy of approximate techniques for strongly correlated electrons that use reduced Hilbert spaces. As a first step, the method involves a change of basis that incorporates exactly part of the short…
Current quantum simulation experiments are starting to explore non-equilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and time scales. Therefore, the question emerges which observables are best suited…
It has been proposed to investigate the equilibration properties of a small isolated quantum system by means of the matrix of asymptotic transition probabilities in some preferential basis. The trace $T$ of this matrix measures the degree…
The dynamics of first-order phase transitions in strongly coupled systems are relevant in a variety of systems, from heavy ion collisions to the early universe. Holographic theories can be used to model these systems, with fluctuations…
We propose and test a scheme for entanglement renormalization capable of addressing large two-dimensional quantum lattice systems. In a translationally invariant system, the cost of simulations grows only as the logarithm of the lattice…
A biorthonormal-block density-matrix renormalization group algorithm is proposed to accurately compute properties of large-scale non-Hermitian many-body systems, in which a renormalized-space partition of the non-Hermitian reduced density…