Related papers: Fast convergence of imaginary time evolution tenso…
Tensor network methods are routinely used in approximating various equilibrium and non-equilibrium scenarios, with the algorithms requiring a small bond dimension at low enough time or inverse temperature. These approaches so far lacked a…
Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size…
The intuitiveness of the tensor network graphical language is becoming well known through its use in numerical simulations using methods from tensor network algorithms. Recent times have also seen rapid progress in developing equations of…
Describing non-equilibrium properties of quantum many-body systems is challenging due to high entanglement in the wavefunction. We describe evolution of local observables via the influence matrix (IM), which encodes the effects of a…
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in…
The approximate contraction of a Projected Entangled Pair States (PEPS) tensor network is a fundamental ingredient of any PEPS algorithm, required for the optimization of the tensors in ground state search or time evolution, as well as for…
We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the {\em projected entangled-pair state} algorithm for finite lattice systems [F. Verstraete and J.I. Cirac,…
Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d)…
We consider the approximation of the ground state of the one-dimensional cubic nonlinear Schr{\"o}dinger equation by a normalized gradient algorithm combined with linearly implicit time integrator, and finite difference space approximation.…
The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their…
Strongly correlated layered 2D systems are of central importance in condensed matter physics, but their numerical study is very challenging. Motivated by the enormous successes of tensor networks for 1D and 2D systems, we develop an…
We simulate a free dissipative and coherent-driven Kerr nonlinear system using a time-evolving block decimation (TEBD) algorithm, to study the impact of the initial state on the exact quantum dynamics of the system. The superposition of two…
We propose a new method for computing the ground state properties and the time evolution of infinite chains based on a transverse contraction of the tensor network. The method does not require finite size extrapolation and avoids explicit…
Understanding dissipation in 2D quantum many-body systems is a remarkably difficult open challenge. Here we show how numerical simulations for this problem are possible by means of a tensor network algorithm that approximates steady-states…
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…
The simple update (SU) and full update (FU) are the two paradigmatic time evolution algorithms for a tensor network known as the infinite projected entangled pair state (iPEPS). They differ by an error measure that is either, respectively,…
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite…
To validate the second-by-second dynamics of turbines in field experiments, it is necessary to accurately reconstruct the winds going into the turbine. Current time-resolved inflow reconstruction techniques estimate wind behavior in…
Belief propagation is a well-studied algorithm for approximating local marginals of multivariate probability distribution over complex networks, while tensor network states are powerful tools for quantum and classical many-body problems.…
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017)]. By encoding the truth table of each vertex…