Related papers: Three-dimensional isometric tensor networks
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…
We propose an environment recycling scheme to speed up a class of tensor network algorithms that produce an approximation to the ground state of a local Hamiltonian by simulating an evolution in imaginary time. Specifically, we consider the…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
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…
In recent years, tree tensor network methods have proven capable of simulating quantum many-body and other high-dimensional systems. This work is a user guide to our Python library PyTreeNet. It includes code examples and exercises to…
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…
Quantum phase transitions between different topologically ordered phases exhibit rich structures and are generically challenging to study in microscopic lattice models. In this work, we propose a tensor-network solvable model that allows us…
We propose an efficient algorithm for simulating quantum many-body systems in two spatial dimensions using projected entangled pair states. This is done by approximating the environment, arising in the context of updating tensors in the…
We determine the computational power of isometric tensor network states (isoTNS), a variational ansatz originally developed to numerically find and compute properties of gapped ground states and topological states in two dimensions. By…
We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops…
We introduce an adaptive-weighted tree tensor network, for the study of disordered and inhomogeneous quantum many-body systems. This ansatz is assembled on the basis of the random couplings of the physical system with a procedure that…
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…
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…
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…
A promising application of neural-network quantum states is to describe the time dynamics of many-body quantum systems. To realize this idea, we employ neural-network quantum states to approximate the implicit midpoint rule method, which…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
We have developed an efficient tensor network algorithm for spin ladders, which generates ground-state wave functions for infinite-size quantum spin ladders. The algorithm is able to efficiently compute the ground-state fidelity per lattice…
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
We introduce tensor field neural networks, which are locally equivariant to 3D rotations, translations, and permutations of points at every layer. 3D rotation equivariance removes the need for data augmentation to identify features in…
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…