Related papers: Optimized Decimation of Tensor Networks with Super…
Tensor networks, such as matrix product states (MPS) and tree tensor network states (TTNS), are powerful ans\"atze for simulating quantum dynamics. While both ans\"atze are theoretically exact in the limit of large bond dimensions, [J.…
Tensor network algorithms have proven to be very powerful tools for studying one- and two-dimensional quantum many-body systems. However, their application to three-dimensional (3D) quantum systems has so far been limited, mostly because…
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the differential geometry underlying TTNs. Building on this foundation, we develop…
Tensor network methods have become a powerful class of tools to capture strongly correlated matter, but methods to capture the experimentally ubiquitous family of models at finite temperature beyond one spatial dimension are largely…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
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…
In this work, a simple and fundamental numeric scheme dubbed as ab-initio optimization principle (AOP) is proposed for the ground states of translational invariant strongly-correlated quantum lattice models. The idea is to transform a…
This paper explores the application of tensor networks (TNs) to the simulation of material deformations within the framework of linear elasticity. Material simulations are essential computational tools extensively used in both academic…
We investigate the disordered spin-$\frac12$Heisenberg model in two dimensions and employ tree tensor networks (TTNs) with a physics-informed structural optimization of the tree layout, to simulate dynamics in the many-body localization…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
We have proposed a novel numerical method to calculate accurately the physical quantities of the ground state with the tensor-network wave function in two dimensions. We determine the tensor network wavefunction by a projection approach…
We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network…
We develop a strategy for tensor network algorithms that allows to deal very efficiently with lattices of high connectivity. The basic idea is to fine-grain the physical degrees of freedom, i.e., decompose them into more fundamental units…
Accurate simulations of the two-dimensional (2D) Hubbard model constitute one of the most challenging problems in condensed matter and quantum physics. Here we develop a tangent space tensor renormalization group (tanTRG) approach for the…
This paper presents a novel, mathematically rigorous framework for autoencoder-type deep neural networks that combines optimal control theory and low-rank tensor methods to yield memory-efficient training and automated architecture…
We introduce the concept of concatenated tensor networks to efficiently describe quantum states. We show that the corresponding concatenated tensor network states can efficiently describe time evolution and possess arbitrary block-wise…
Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…
The infinite time-evolving block decimation (iTEBD) algorithm [Phys. Rev. Lett. 98, 070201 (2007)] allows to simulate unitary evolution and to compute the ground state of one-dimensional quantum lattice systems in the thermodynamic limit.…
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…
In this paper, we study the nonnegative tensor data and propose an orthogonal nonnegative Tucker decomposition (ONTD). We discuss some properties of ONTD and develop a convex relaxation algorithm of the augmented Lagrangian function to…