Disorder-aware neural quantum states provide the first microscopic evidence for a pinned hole Wigner crystal near ν=2/3 that accounts for reentrant integer quantum Hall physics and reveals an electron-hole asymmetry in crystallization.
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von Glehn, J
16 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We present a novel neural network architecture using self-attention, the Wavefunction Transformer (Psiformer), which can be used as an approximation (or Ansatz) for solving the many-electron Schr\"odinger equation, the fundamental equation for quantum chemistry and material science. This equation can be solved from first principles, requiring no external training data. In recent years, deep neural networks like the FermiNet and PauliNet have been used to significantly improve the accuracy of these first-principle calculations, but they lack an attention-like mechanism for gating interactions between electrons. Here we show that the Psiformer can be used as a drop-in replacement for these other neural networks, often dramatically improving the accuracy of the calculations. On larger molecules especially, the ground state energy can be improved by dozens of kcal/mol, a qualitative leap over previous methods. This demonstrates that self-attention networks can learn complex quantum mechanical correlations between electrons, and are a promising route to reaching unprecedented accuracy in chemical calculations on larger systems.
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cond-mat.str-el 4 quant-ph 4 cond-mat.dis-nn 2 cond-mat.quant-gas 1 cond-mat.supr-con 1 cs.LG 1 nucl-th 1 physics.chem-ph 1 physics.comp-ph 1roles
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background 1representative citing papers
VMC's gradient estimators are generically heavy-tailed (no 3/2 moment for Slater–Jastrow); PS-Clip-VMC, which clips energies and per-sample gradients, is provably convergent under weak moments and stabilizes FermiNet training.
First NQS variational Monte Carlo calculation of excited states in A=4 nuclei and hypernuclei, reproducing benchmarks and providing the first ab initio M1 transition strength for ^{4}_ΛH consistent with weak-coupling limit at 1.3% suppression.
A new neural quantum state ansatz for bosons in the grand canonical ensemble achieves competitive variational energies in 1D and 2D systems and provides access to one-body reduced density matrices.
Fermi Sets achieve universal approximation of fermionic wavefunctions using K antisymmetric bases times symmetric neural networks, where K equals 1 in 1D, 2 in 2D, and grows linearly with particle number in higher dimensions.
Self-attention variational wavefunctions for the 2D homogeneous electron gas up to N=169 yield energies below DMC and a converged collective-mode dispersion including a roton-like minimum.
A unified structured factorization framework for quantum state tomography that parametrizes the density matrix as FF^dagger, supports multiple priors, provides sample complexity bounds, and introduces projected gradient descent and power-method algorithms.
HI-NQS uses a dual-channel autoregressive Transformer NQS inside an iterative sample-diagonalize-update loop to reach chemical accuracy on small molecules and nitrogen active spaces with better determinant scaling than CIPSI.
Projected Inverse Iteration reframes ground-state search for neural quantum states as an eigenvalue problem to deliver rapid, spectral-gap-insensitive convergence while retaining polynomial scaling.
Transformer wave functions for the J1-J2 Heisenberg model exhibit size-independent power-law decay of V-score with compute, with the exponent decreasing as frustration increases.
Variational optimization of quantum ground states represented as SIC-POVM outcome probabilities using GRU autoregressive networks, tested on 1D Ising and Heisenberg models up to L=128.
Neural wave functions uncover FFLO, polarized superfluid, phase-separated, and crystalline Cooper-pair phases in the 2D spin-imbalanced Fermi gas.
A learnable Gaussian-basis locality parameter α lowers NNVMC variational energies on the 3D electron gas and sharpens the Fermi-liquid–Wigner-crystal transition for message-passing ansatze.
A general-purpose self-attention Fermi neural network finds chiral p_x ± ip_y superconductivity in an attractive Fermi gas via unbiased energy minimization.
NN-fTNS enhance fermionic tensor networks with neural parametrization to improve expressivity and achieve order-of-magnitude better energies than pure fTNS on Hubbard models while maintaining linear scaling.
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Crystallization in the Fractional Quantum Hall Regime with Disorder-Aware Neural Quantum States
Disorder-aware neural quantum states provide the first microscopic evidence for a pinned hole Wigner crystal near ν=2/3 that accounts for reentrant integer quantum Hall physics and reveals an electron-hole asymmetry in crystallization.
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Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimization
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Projected Inverse Iteration: An Eigenvalue Approach to Ground-State Computation with Neural Quantum States
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Uncovering Exotic Paired States in the 2D Spin-Imbalanced Fermi Gas with Neural Wave Functions
Neural wave functions uncover FFLO, polarized superfluid, phase-separated, and crystalline Cooper-pair phases in the 2D spin-imbalanced Fermi gas.
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Enhancing Neural-Network Variational Monte Carlo through Basis Transformation
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Attention is all you need to solve chiral superconductivity
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