Related papers: Efficient Simulation of Dynamics in Two-Dimensiona…

Tensor networks provide a powerful tool for studying many-body quantum systems, particularly making quantum simulations more efficient. In this article, we construct a tensor network representation of the spin network states, which…

Tensor Networks are non-trivial representations of high-dimensional tensors, originally designed to describe quantum many-body systems. We show that Tensor Networks are ideal vehicles to connect quantum mechanical concepts to machine…

Tree tensor network states (TTNSs) combined with the density matrix renormalization group (DMRG) are emerging as powerful tools for vibrational and vibronic structure simulations in molecules with strong coupling and fluxionality. In this…

Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…

We develop a density matrix renormalization group (DMRG) algorithm for constrained quantum lattice models that successfully {\it{implements the local constraints as symmetries in the contraction of the matrix product states and matrix…

An efficient algorithm is constructed for contracting two-dimensional tensor networks under periodic boundary conditions. The central ingredient is a novel renormalization step that scales linearly with system size, i.e. from $L \to L+1$.…

Using a recently developed extension of the time-dependent variational principle for matrix product states, we evaluate the dynamics of 2D power-law interacting XXZ models, implementable in a variety of state-of-the-art experimental…

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.…

The one-dimensional Ising model with its connections to several physical concepts plays a vital role in comprehension of several principles, phenomena and numerical methods. The Hamiltonian of a coupled one-dimensional dissipative spin…

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a…

We propose a tensor-network algorithm for discrete-time stochastic dynamics of a homogeneous system in the thermodynamic limit. We map a $d$-dimensional nonequilibrium Markov process to a $(d+1)$-dimensional infinite tensor network by using…

We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using Matrix Product States (MPS) and Matrix Product Operators (MPOs). We explore the bulk phase diagram of the theory on regular tessellations of hyperbolic space…

We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolutions given by a generic master equation. Its two…

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…

This paper presents a systematic study of the application of convolutional neural networks (CNNs) as an efficient and versatile tool for the analysis of critical and low-temperature phase states in spin system models. The problem of…

We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…

Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…

An efficient algorithm is developed for quantum spin tubes in the context of the tensor network representations. It allows to efficiently compute the ground-state fidelity per lattice site, which in turn enables us to identify quantum…

Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state…

Predicting the quantum dynamics of promising solid-state and molecular quantum technology candidates remains a formidable challenge. Yet, accessing these dynamics is key to understanding and controlling decoherence mechanisms -- a…