Related papers: Intrinsic dimension of path integrals: data mining…
The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…
The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the…
A real-time path integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the…
To gain insight into the mechanisms behind machine learning methods, it is crucial to establish connections among the features describing data points. However, these correlations often exhibit a high-dimensional and strongly nonlinear…
The influence matrix (IM) provides a powerful framework for characterizing nonequilibrium quantum many-body dynamics by encoding multitime correlations into tensor-network states. Understanding how its computational complexity relates to…
The path-integral formulation of the statistical mechanics of quantum many-body systems is described, with the purpose of introducing practicaltechniques for the simulation of solids. Monte Carlo and molecular dynamics methods for…
The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or…
Inspired by the close relationship between Kolmogorov complexity and unsupervised machine learning, we explore quantum circuit complexity, an important concept in quantum computation and quantum information science, as a pivot to understand…
The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…
Understanding the real time dynamics of quantum systems without quasiparticles constitutes an important yet challenging problem. We study the superfluid-insulator quantum-critical point of bosons on a two-dimensional lattice, a system whose…
We review methods that allow one to detect and characterise quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without…
Identifying and classifying quantum phases from measurable time series in many-body dynamics have significant values, yet face formidable challenges, requiring profound knowledge of physicists. Here, to achieve a pure data-driven machine…
In a number of classical statistical-physical models, there exists a characteristic dimensionality called the upper critical dimension above which one observes the mean-field critical behavior. Instead of constructing high-dimensional…
We present a quantum Monte Carlo-based approach to detect and compute the most dominant correlations for many-body systems without prior knowledge. It is based on the measurement and analysis of the correlation density matrix between two…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
An efficient Path Integral Monte Carlo procedure is proposed to simulate the behavior of quantum many-body dissipative systems described within the framework of the influence functional. Thermodynamic observables are obtained by Monte Carlo…
Scrambling unitary dynamics in a quantum system transmutes local quantum information into a non-local web of correlations which manifests itself in a complex spatio-temporal pattern of entanglement. In such a context, we show there can…
Molecular dynamics (MD) simulations provide atomistic insights into the structure, dynamics, and function of biomolecules by generating time-resolved, high-dimensional trajectories. Analyzing such data benefits from estimating the minimal…
We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for small number of atoms, which permits us to…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…