Understanding dynamical properties of quantum many-body systems remains a central challenge because excitations generally require information beyond a ground-state wave function. Here we introduce a neural polaron ansatz that represents quasiparticle excitations by neural many-body operators acting on a correlated ground state. Instead of learning an independent excited-state wave function, the method parameterizes a local dressing operator through a compact neural head defined on the feature map of a pretrained ground-state network. This operator-based construction builds in translation symmetry, momentum resolution, and quasiparticle locality, while separating ground-state correlations from excitation-specific dressing. We benchmark the method on the square-lattice $J_1$-$J_2$ Heisenberg model, where it accurately reproduces magnon dispersions and spectral weights over a broad range of frustration. In particular, it captures nontrivial many-body features including the $(π,0)$ anomaly and its progressive softening with increasing $J_2/J_1$. These results establish neural operators as a physically transparent route for extending neural quantum states from ground-state properties to dynamical response.
Understanding dynamical properties of quantum many-body systems remains a central challenge because excitations generally require information beyond a ground-state wave function. Here we introduce a neural polaron ansatz that represents quasiparticle excitations by neural many-body operators acting on a correlated ground state. Instead of learning an independent excited-state wave function, the method parameterizes a local dressing operator through a compact neural head defined on the feature map of a pretrained ground-state network. This operator-based construction builds in translation symmetry, momentum resolution, and quasiparticle locality, while separating ground-state correlations from excitation-specific dressing. We benchmark the method on the square-lattice J1-J2 Heisenberg model, where it accurately reproduces magnon dispersions and spectral weights over a broad range of frustration. In particular, it captures nontrivial many-body features including the (π,0) anomaly and its progressive softening with increasing J2/J1. These results establish neural operators as a physically transparent route for extending neural quantum states from ground-state properties to dynamical response.
The use of artificial neural networks to represent quantum wave functions has recently attracted interest as a way to solve complex many-body problems. The potential of these variational parametrizations has been supported by analytical and numerical evidence in controlled benchmarks. While approaching the end of the early research phase in this field, it becomes increasingly important to show how neural-network states perform for models and physical problems that constitute a clear open challenge for other many-body computational methods. In this paper, we start addressing this aspect, concentrating on a presently unsolved model describing two-dimensional frustrated magnets. Using a fully convolutional neural network model as a variational ans\"atz, we study the frustrated spin-1/$2{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the square lattice. We demonstrate that the resulting predictions for both ground-state energies and properties are competitive with, and often improve upon, existing state-of-the-art methods. In a relatively small region in the parameter space, corresponding to the maximally frustrated regime, our ans\"atz exhibits comparatively good but not the best performance. The gap between the complexity of the models adopted here and those routinely adopted in deep-learning applications is, however, still substantial, such that further improvements in future generations of neural-network quantum states are likely to be expected.
In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high precision the ground states of some notable quantum many-body systems. We consider the one-dimensional free bosons and fermions, spinless fermions on a square lattice away from half-filling, as well as frustrated quantum magnetism with a rapidly oscillating ground-state characteristic function. In the latter case, an ANN with a standard architecture fails, while that with a slightly modified one successfully learns the frustration-induced complex sign rule in the ground state and approximates the ground states with high precisions. As an example of practical use of our method, we also perform the variational method to explore the ground state of an antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model.
Neural quantum states provide a flexible and scalable framework for strongly correlated systems. This thesis develops and benchmarks variational neural ansÀtze for fermionic lattice models, targeting ground states and low-lying excited states, with a particular focus on architectural performance. The constructions embed known structure such as fermionic antisymmetry, lattice translations, and total momentum while learning the remaining correlations efficiently in log amplitude. In the first part, we introduce a single dimensionless, intensive accuracy indicator, the V-score. Defined from the mean energy and energy variance of a state, it enables objective, method-agnostic comparisons across system sizes, interaction strengths, and even distinct momentum sectors, including regimes without exact references. We use it as a unifying measure of variational quality throughout the thesis. In the second part, we introduce a symmetry-aware Slaterâ Backflowâ Jastrow ansatz for spinless fermions in the t-V model. A convolutional backflow is built to be translation equivariant and consistent with particle exchange, allowing quantum-number projection to a fixed momentum without additional forward passes. This state is used to target ground states and momentum-resolved excitations, and to probe ordering tendencies via structure factors. In the third part, we develop a momentum-projected vision-transformer ansatz (DefeViT) for the one-hole t-J family. The state is factorized in a fixed-hole frame with a neural amplitude for the mobile defect, then restored to a chosen total momentum by summing lattice translations with the appropriate fermionic phase. On square lattices and their diagonal extensions (t'-J'), the approach captures ground-state properties and single-hole dispersions and tracks how spin correlators and hole-centered bond textures evolve under frustration. Within this setting, physics-informed neural states provide compact and accurate descriptions of ground states and low-lying excited states.
We introduce Neural Tensor Network States (νTNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the νTNS framework, a neural network serves as a disentangler of the wave-function, transforming the physical degrees of freedom into renormalized variables with much less entanglement. The renormalized state is then efficiently encoded by a back-flow tensor network. This construction yields a compact yet highly expressive representation of strongly correlated quantum states. Using convolutional neural networks combined with matrix product states as a concrete implementation, we obtain state-of-the-art variational energies for the spin-1/2J1-J2 Heisenberg model on the square lattice at the highly frustrated point J2/J1=0.5, for systems up to 20×20 with periodic boundary conditions. Finite-size scaling of spin, dimer, and plaquette correlations exhibits power-law decay without magnetic or valence-bond long-range order, consistent with a gapless quantum spin-liquid ground state at that point.This νTNS framework is flexible and naturally extensible to other neural and tensor-network structures, offering a general platform for investigating strongly correlated quantum many-body systems.
Understanding strongly correlated quantum many-body systems requires dealing with a largeconfiguration space comprised of a set of all possible measurable configurations. The total number of configurations grows exponentially with the size of the system, which makes exact numerical calculations impossible for even moderately sized systems. Since the advent of high-temperature superconductivity and the subsequent interest in strongly correlated phases of matter, progress in the field has been marked by ingenuity of the field to overcome these computational limitations. The first techniques to emerge were inspired by quantum chemistry and based on exact diagonalization[1], which is limited to small clusters, and different variants of quantum Monte Carlo[2], that suffers from the sign problem in fermionic and frustrated systems. Circa 1992, the density matrix renormalization group (DMRG) [3, 4, 5, 6, 7] became one of the major breakthroughs of the past few decades. Despite the success of DMRG for one-dimensional(1D) and quasi-one-dimensional geometries, extensions to actual two-dimensional systems remain challenging and applications are constrained to long cylinders and strips. One promising alternative is to combine one the oldest methods, variational wave functions (VWFs), with neural networks, which have been used to recently with great success in machine learning. The focus of this dissertation is on developing novel variational Monte Carlo algorithms to make neural network variational wave functions applicable to many problems in quantum many-body physics. These algorithms draw from existing variational wave-function, tensor network, and machine learning methods. We calculate dynamical spectral functions using the vector correction and Chebyshev expansion method. We do finite temperature calculations with minimally entangled thermal states. Finally, we do ground state calculations for the frustrated J1−J2 Heisenberg model. We benchmark these results using restricted Boltzmann machines as the neural network for the the variational wave-functions.--Author's abstract
Variational representations of quantum states abound and have successfully been used to guess ground-state properties of quantum many-body systems. Some are based on partial physical insight (Jastrow, Gutzwiller-projected, and fractional quantum Hall states, for instance), and others operate as a black box that may contain information about the underlying structure of entanglement and correlations (tensor networks, neural networks) and offer the advantage of a large set of variational parameters that can be efficiently optimized. However, using variational approaches to study excited states and, in particular, calculating the excitation spectrum, remains a challenge. We present a variational method to calculate the dynamical properties and spectral functions of quantum many-body systems in the frequency domain, where the Green's function of the problem is encoded in the form of a restricted Boltzmann machine (RBM). We introduce a natural gradient descent approach to solve linear systems of equations and use Monte Carlo to obtain the dynamical correlation function. In addition, we propose a strategy to regularize the results that improves the accuracy dramatically. As an illustration, we study the dynamical spin structure factor of the one dimensional ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. The method is general and can be extended to other variational forms.