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We introduce a new family of trial wave-functions based on deep neural networks to solve the many-electron Schr\"odinger equation. The Pauli exclusion principle is dealt with explicitly to ensure that the trial wave-functions are physical.…

Computational Physics · Physics 2020-07-21 Jiequn Han , Linfeng Zhang , Weinan E

It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…

General Physics · Physics 2020-02-12 Edward Belbruno

Preparing quantum many-body states on classical or quantum devices is a very challenging task that requires accounting for exponentially large Hilbert spaces. Although this complexity can be managed with exponential ans\"atze (such as in…

Quantum Physics · Physics 2024-11-13 Weillei Zeng , Jiaji Zhang , Lipeng Chen , Carlos L. Benavides-Riveros

The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the non-trivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that…

Disordered Systems and Neural Networks · Physics 2017-02-13 Giuseppe Carleo , Matthias Troyer

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…

Disordered Systems and Neural Networks · Physics 2025-12-23 Lars Humpert , Dante M. Kennes , Jan-Niklas Herre

The integration of deep neural networks with the Variational Monte Carlo (VMC) method has marked a significant advancement in solving the Schr\"odinger equation. In this work, we enforce spin symmetry in the neural network-based VMC…

Chemical Physics · Physics 2024-06-04 Zhe Li , Zixiang Lu , Ruichen Li , Xuelan Wen , Xiang Li , Liwei Wang , Ji Chen , Weiluo Ren

Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct application of the tensor train method typically requires…

Numerical Analysis · Mathematics 2025-10-16 Yani Feng , Michael K. Ng , Kejun Tang , Zhiwen Zhang

In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…

Number Theory · Mathematics 2024-08-27 Kushal Dhar Dwivedi , Anup Singh

Due to the presence of strong correlations, theoretical or experimental investigations of quantum many-body systems belong to the most challenging tasks in modern physics. Stimulated by tensor networks, we propose a scheme of constructing…

Strongly Correlated Electrons · Physics 2017-10-17 Shi-Ju Ran , Angelo Piga , Cheng Peng , Gang Su , Maciej Lewenstein

Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…

Strongly Correlated Electrons · Physics 2026-05-14 Jian-Gang Kong , Jia-Ji Zhu , Z. Y. Xie

The term Tensor Network States (TNS) refers to a number of families of states that represent different ans\"atze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case…

High Energy Physics - Lattice · Physics 2014-02-04 Mari Carmen Bañuls , Krzysztof Cichy , J. Ignacio Cirac , Karl Jansen , Hana Saito

A combination of the variable-constant and complex coordinate rotation methods is used to solve the two-body Schr\"odinger equation. The latter is replaced by a system of linear first-order differential equations, which enables one to…

Nuclear Theory · Physics 2008-11-26 S. A. Rakityansky , S. A. Sofianos , K. Amos

We discuss in detail algorithms for implementing tensor network renormalization (TNR) for the study of classical statistical and quantum many-body systems. Firstly, we recall established techniques for how the partition function of a 2D…

Strongly Correlated Electrons · Physics 2017-01-18 Glen Evenbly

Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…

Computational Physics · Physics 2026-02-13 Lorenzo Brevi , Antonio Mandarino , Carlo Barbieri , Enrico Prati

The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…

Disordered Systems and Neural Networks · Physics 2021-05-12 Chen-Yu Liu , Daw-Wei Wang

Given access to accurate solutions of the many-electron Schr\"odinger equation, nearly all chemistry could be derived from first principles. Exact wavefunctions of interesting chemical systems are out of reach because they are NP-hard to…

Chemical Physics · Physics 2021-03-26 David Pfau , James S. Spencer , Alexander G. de G. Matthews , W. M. C. Foulkes

We study the three-body systems $DNN$ and $D^{*}NN$ within a hadronic molecular framework by combining a realistic nucleon-nucleon interaction with a $D^{(*)}N$ potential constrained by heavy-quark symmetry. The three-body Schr\"odinger…

High Energy Physics - Phenomenology · Physics 2026-05-25 Si-Yi Chen , Fei-Yu Chen , Xu-Liang Chen , Lu Meng , Ning Li , Wei Chen

We combine density-functional tight-binding (DFTB) with deep tensor neural networks (DTNN) to maximize the strengths of both approaches in predicting structural, energetic, and vibrational molecular properties. The DTNN is used to learn a…

Chemical Physics · Physics 2020-06-19 Martin Stöhr , Leonardo Medrano Sandonas , Alexandre Tkatchenko

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…

Strongly Correlated Electrons · Physics 2015-06-15 Zhen Wang , Yongjian Han , Guang-Can Guo , Lixin He

We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…

Quantum Physics · Physics 2023-03-02 Kouichi Okunishi , Hiroshi Ueda , Tomotoshi Nishino