Related papers: Tree tensor networks and entanglement spectra
We show that the entanglement structure of quantum many-body states defines a natural and optimal distributed representation for their simulation. An arbitrary entanglement cut induces a bipartite decomposition of the wavefunction, mapping…
Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here we put forward a variational Monte Carlo approach for the…
A tensor network is a diagram that specifies a way to "multiply" a collection of tensors together to produce another tensor (or matrix). Many existing algorithms for tensor problems (such as tensor decomposition and tensor PCA), although…
Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely…
We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler…
We investigate the global-symmetry projections applied to the tensor network states from the view point of the entanglement entropy and the mutual information. The projections to the translational invariant space and to the total-$S^z$-zero…
Recently developed tensor network methods demonstrate great potential for addressing the quantum many-body problem, by constructing variational spaces with polynomially, instead of exponentially, scaled parameters. Constructing such an…
Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…
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 describe a numerical many-body technique that is based on both tensor networks and quantum Monte Carlo. The variational ansatz is a tensor network that can harvest volume-law entanglement. It is constructed from a tensor train to which…
We introduce a novel class of phase transitions separating quantum states with different entanglement features. An example of such an "entanglement phase transition" is provided by the many-body localization transition in disordered quantum…
Variational tensor network optimization has become a powerful tool for studying classical statistical models in two dimensions. However, its application to three-dimensional systems remains limited, primarily due to the high computational…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an…
A rigorous analysis is presented for the entanglement spectrum of quantum many-body states possessing a higher-form group-representation symmetry generated by topological Wilson loops, which is generally non-invertible. A general framework…
The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…
We introduce a numerical framework for integrating Markovian dynamics on tree tensor operator (TTO) ansatz states. This framework enables the simulation of both transient and steady-state regimes of systems governed by the Lindblad master…
Tensor networks are the main building blocks in a wide variety of computational sciences, ranging from many-body theory and quantum computing to probability and machine learning. Here we propose a parallel algorithm for the contraction of…