Related papers: A tensor network approach to 2D bosonization
Simulating many-body open quantum systems is an extremely challenging problem, with methods often restricted to either models with nearest-neighbor interactions or semi-classical approximations. In particular, modeling two-dimensional…
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…
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…
Recent work has shown that for one-dimensional quantum states that can be effectively approximated by matrix product operators (MPOs), a polynomial number of copies of the state suffices for reconstruction. Compared to MPOs in one…
The performance of deep neural networks (DNN) is very sensitive to the particular choice of hyper-parameters. To make it worse, the shape of the learning curve can be significantly affected when a technique like batchnorm is used. As a…
Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…
Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural…
Tensor networks provide an efficient approximation of operations involving high dimensional tensors and have been extensively used in modelling quantum many-body systems. More recently, supervised learning has been attempted with tensor…
The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…
This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of…
We construct novel fermion-fermion dualities in $2+1$-dimensions using 3d bosonization dualities. This is achieved by relating two-node quiver theories using both the flavor-bounded and flavor-violated 3d bosonization dualities. Such…
Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression…
Due to the unfavorable scaling of tensor network methods with the refinement parameter M, new approaches are necessary to improve the efficiency of numerical simulations based on such states in particular for gapless, strongly entangled…
This paper proposes a deep Convolutional Neural Network(CNN) with strong generalization ability for structural topology optimization. The architecture of the neural network is made up of encoding and decoding parts, which provide down- and…
We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…
General results on the structure of the bosonization of fermionic systems in $(2+1)$d are obtained. In particular, the universal character of the bosonized topological current is established and applied to generic fermionic current…
In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show…
This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…
Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…