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Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
Many-body localization (MBL) can occur when strong disorders prevent an interacting system from thermalization. To study the dynamics of such systems, it is typically necessary to perform an ensemble average over many different disorder…
We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show…
Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically…
The variational cluster approach (VCA) is applied to the one-dimensional Hubbard model at zero temperature using clusters (chains) of up to ten sites with full diagonalization and the Lanczos method as cluster solver. Within the framework…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
A new numerical algorithm for interacting fermion systems to treat the grand-canonical ensemble is proposed and examined by extending the path-integral renormalization group method. To treat the grand-canonical ensemble, the particle-hole…
Rerandomization utilizes modern computing ability to improve covariate balance while adhering to the randomization principle originally advocated by RA Fisher. Affinely invariant rerandomization has the ``Equal Percent Variance Reducing''…
Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their…
The method used earlier for analysis of correlated nanoscopic systems is extended to infinite (periodic) s-band like systems described by the Hubbard model and its extensions. The optimized single-particle wave functions contained in the…
$\ell_1$ optimization is a well known heuristic often employed for solving various forms of sparse linear problems. In this paper we look at its a variant that we refer to as the \emph{partial} $\ell_1$ and discuss its mathematical…
We present a novel Monte Carlo algorithm which enhances equilibrization of low-temperature simulations and allows sampling of configurations over a large range of energies. The method is based on a non-Boltzmann probability weight factor…
This paper presents a renormalization approach to many-particle systems. By starting from a bare Hamiltonian ${\cal H}= {\cal H}_0 +{\cal H}_1$ with an unperturbed part ${\cal H}_0$ and a perturbation ${\cal H}_1$,we define an effective…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact…
We extend to quenched disordered systems the variational scheme for real space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow…
The characterizing feature of a many-body localized phase is the existence of an extensive set of quasi-local conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in…
Large systems of linear equations are ubiquitous in science. Quite often, e.g. when considering population dynamics or chemical networks, the solutions must be non-negative. Recently, it has been shown that large systems of random linear…
The finite-amplitude method (FAM) is one of the most promising methods for optimizing the computational performance of the random-phase approximation (RPA) calculations in deformed nuclei. In this report, we will mainly focus on our recent…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…