Related papers: Numerical continuum tensor networks in two dimensi…
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular class of TNS and are used for the simulation of…
Tensor networks provide discrete representations of quantum many-body systems, yet their precise connection to continuum field theories remains relatively poorly understood. Invoking a notion of typicality, we develop a continuum…
Tensor Network States are ans\"atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation…
We study pairing of an interacting three component Fermi gas in two dimensions. By using a mean field theory to decouple the interactions between different pairs of Fermi components, we study the free energy landscapes as a function of…
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement…
Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
In many cases, Neural networks can be mapped into tensor networks with an exponentially large bond dimension. Here, we compare different sub-classes of neural network states, with their mapped tensor network counterpart for studying the…
We propose a simple connection between matrix quantum mechanics and tensor networks. This allows us to imbue tensor networks with some interesting additional structure. The geometry of the graph describing the tensor network state is…
Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised…
Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in…
The dynamics of plasmas are governed by a set of non-linear differential equations which remain challenging to solve directly for large 2D and 3D problems. Here we investigate how tensor networks could be applied to plasmas described by the…
Infinite projected entangled pair states (iPEPS) have emerged as a powerful tool for studying interacting two-dimensional fermionic systems. In this review, we discuss the iPEPS construction and some basic properties of this tensor network…
We consider two (2D) and three (3D) dimensional granular systems exposed to compression, and ask what is the influence of the number of physical dimensions on the properties of the interaction networks that spontaneously form as these…
Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this…
The simulation of lattice gauge theories with tensor network (TN) methods is becoming increasingly fruitful. The vision is that such methods will, eventually, be used to simulate theories in $(3+1)$ dimensions in regimes difficult for other…
We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks,…
Tensor network methods provide an intuitive graphical language to describe quantum states, channels, open quantum systems and a class of numerical approximation methods that efficiently simulate certain many-body states in one spatial…
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…
We describe a class of neuralized fermionic tensor network states (NN-fTNS) that introduce non-linearity into fermionic tensor networks through configuration-dependent neural network transformations of the local tensors. The construction…
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…