Related papers: Efficient representation of fully many-body locali…

Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions,…

Many-body localized (MBL) systems are often described using their local integrals of motion, which, for spin systems, are commonly assumed to be a local unitary transform of the set of on-site spin-z operators. We show that this assumption…

We employ a convolutional neural network to explore the distinct phases in random spin systems with the aim to understand the specific features that the neural network chooses to identify the phases. With the energy spectrum normalized to…

Establishing a predictive ab initio method for solid systems is one of the fundamental goals in condensed matter physics and computational materials science. The central challenge is how to encode a highly-complex quantum-many-body wave…

We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…

High throughput screening of materials for technologically relevant areas, like identification of better catalysts, electronic materials, ceramics for high temperature applications and drug discovery, is an emerging topic of research. To…

This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert…

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost…

Calculation of observables with three-dimensional projected entangled pair states is generally hard, as it requires a contraction of complex multi-layer tensor networks. We utilize the multi-layer structure of these tensor networks to…

Deep neural networks have demonstrated remarkable efficacy in extracting meaningful representations from complex datasets. This has propelled representation learning as a compelling area of research across diverse fields. One interesting…

By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make…

We adapt a machine-learning approach to study the many-body localization transition in interacting fermionic systems on disordered 1D and 2D lattices. We perform supervised training of convolutional neural networks (CNNs) using labelled…

Quantum many-body physics simulation has important impacts on understanding fundamental science and has applications to quantum materials design and quantum technology. However, due to the exponentially growing size of the Hilbert space…

We prove the existence of extensive many-body Hamiltonians with few-body interactions and a many-body mobility edge: all eigenstates below a nonzero energy density are localized in an exponentially small fraction of "energetically allowed…

Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to…

The fully anisotropic two-leg spin-1/2 $XXZ$ ladder model is studied in terms of an algorithm based on the tensor network representation of quantum many-body states as an adaptation of projected entangled pair states to the geometry of…

Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…

We describe N-body networks, a neural network architecture for learning the behavior and properties of complex many body physical systems. Our specific application is to learn atomic potential energy surfaces for use in molecular dynamics…

Understanding quantum systems is of significant importance for assessing the performance of quantum hardware and software, as well as exploring quantum control and quantum sensing. An efficient representation of quantum states enables…

We apply a series of projection techniques on top of tensor networks to compute energies of ground state wave functions with higher accuracy than tensor networks alone with minimal additional cost. We consider both matrix product states as…