First-quantized deep neural network techniques are developed for analyzing strongly coupled fermionic systems on the lattice. Using a Slater-Jastrow-inspired ansatz which exploits deep residual networks with convolutional residual blocks, we approximately determine the ground state of spinless fermions on a square lattice with nearest-neighbor interactions. The flexibility of the neural-network ansatz results in a high level of accuracy when compared with exact diagonalization results on small systems, both for energy and correlation functions. On large systems, we obtain accurate estimates of the boundaries between metallic and charge-ordered phases as a function of the interaction strength and the particle density.
First-quantized deep neural network techniques are developed for analyzing strongly coupled fermionic systems on the lattice. Using a Slater-Jastrow-inspired ansatz which exploits deep residual networks with convolutional residual blocks, we approximately determine the ground state of spinless fermions on a square lattice with nearest-neighbor interactions. The flexibility of the neural-network ansatz results in a high level of accuracy when compared with exact diagonalization results on small systems, both for energy and correlation functions. On large systems, we obtain accurate estimates of the boundaries between metallic and charge-ordered phases as a function of the interaction strength and the particle density.
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 compute the ground-state properties of fully polarized, trapped, one-dimensional fermionic systems interacting through a Gaussian potential. We use an antisymmetric artificial neural network, or neural quantum state, as an Ansatz for the wave function and use machine learning techniques to variationally minimize the energy of systems from two to six particles. We provide extensive benchmarks for this toy model with other many-body methods, including exact diagonalization and the Hartree-Fock approximation. The neural quantum state provides the best energies across a wide range of interaction strengths. We find very different ground states depending on the sign of the interaction. In the nonperturbative repulsive regime, the system asymptotically reaches crystalline order. In contrast, the strongly attractive regime shows signs of bosonization. The neural quantum state continuously learns these different phases with an almost constant number of parameters and a very modest increase in computational time with the number of particles.
In recent years, neural quantum states have emerged as a powerful variational approach, achieving state-of-the-art accuracy when representing the ground-state wave function of a great variety of quantum many-body systems, including spin lattices, interacting fermions or continuous-variable systems. However, accurate neural representations of the ground state of interacting bosons on a lattice have remained elusive. We introduce a neural backflow Jastrow Ansatz, in which occupation factors are dressed with translationally equivariant many-body features generated by a deep neural network. We show that this neural quantum state is able to faithfully represent the ground state of the 2D Bose-Hubbard Hamiltonian across all values of the interaction strength. We scale our simulations to lattices of dimension up to 20 × 20 while achieving the best variational energies reported for this model. This enables us to investigate the scaling of the entanglement entropy across the superfluid-to-Mott quantum phase transition, a quantity hard to extract with non-variational approaches.
Given access to accurate solutions of the many-electron Schrödinger equation, nearly all chemistry could be derived from first principles.Exact wave functions of interesting chemical systems are out of reach because they are NP-hard to compute in general, but approximations can be found using polynomially scaling algorithms.The key challenge for many of these algorithms is the choice of wave function approximation, or Ansatz, which must trade off between efficiency and accuracy.Neural networks have shown impressive power as accurate practical function approximators and promise as a compact wave-function Ansatz for spin systems, but problems in electronic structure require wave functions that obey Fermi-Dirac statistics.Here we introduce a novel deep learning architecture, the Fermionic neural network, as a powerful wave-function Ansatz for many-electron systems.The Fermionic neural network is able to achieve accuracy beyond other variational quantum Monte Carlo Ansatz on a variety of atoms and small molecules.Using no data other than atomic positions and charges, we predict the dissociation curves of the nitrogen molecule and hydrogen chain, two challenging strongly correlated systems, to significantly higher accuracy than the coupled cluster method, widely considered the most accurate scalable method for quantum chemistry at equilibrium geometry.This demonstrates that deep neural networks can improve the accuracy of variational quantum Monte Carlo to the point where it outperforms other ab initio quantum chemistry methods, opening the possibility of accurate direct optimization of wave functions for previously intractable many-electron systems.
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.
We present a deep neural network (DNN) -based model (HubbardNet) to variationally find the ground-state and excited-state wave functions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with M sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion, U, and the total number of particles, N, from a single training. This approach bypasses the need to solve a new Hamiltonian for each different set of values (U,N) and generalizes well even for out-of-distribution (U,N). Using HubbardNet, we identify the two ground-state phases of the Bose-Hubbard model (Mott insulator and superfluid). We show that the DNN-parametrized solutions are in excellent agreement with results from the exact diagonalization of the Hamiltonian, and it outperforms exact diagonalization in terms of computational scaling. These advantages suggest that our model is promising for efficient and accurate computation of exact phase diagrams of many-body lattice Hamiltonians.