Transformer Neural-Network Quantum States for lattice models of spins and fermions: Application to the Ancilla Layer Model

arXiv:2603.02316 · cond-mat.str-el, cond-mat.dis-nn · Submitted 2026-03-02 · Read on arXiv

cond-mat.str-el, cond-mat.dis-nn

Submitted: 2026-03-02

Updated: 2026-09-17

Terminology

• Transformer — 63× in this paper · explained in 2 episodes
• Hilbert Space — 16× in this paper · explained in 2 episodes
• Accuracy — 14× in this paper · explained in 1 episode
• Ancilla Layer Model — 8× in this paper
• Benchmark — 8× in this paper · explained in 2 episodes
• Transformer Architecture — 8× in this paper · explained in 2 episodes
• Attention Mechanism — 7× in this paper · explained in 2 episodes
• Hubbard Model — 7× in this paper · explained in 3 episodes
• Neural-Network Quantum States — 7× in this paper
• Entanglement — 5× in this paper · explained in 3 episodes
• Tokenization — 5× in this paper · explained in 2 episodes
• Density Matrix Renormalization Group — 4× in this paper
• Entanglement Entropy — 4× in this paper · explained in 2 episodes
• Antiferromagnetism — 3× in this paper · explained in 1 episode
• Benchmarking — 3× in this paper · explained in 3 episodes
• Variational Monte Carlo — 2× in this paper
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Degeneracy — 1× in this paper · explained in 3 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Quantum Physics — 1× in this paper · explained in 10 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Scaling Laws — 1× in this paper · explained in 4 episodes
• Transferability — 1× in this paper · explained in 4 episodes
• Variational Monte Carlo (VMC) — 1× in this paper · explained in 2 episodes

Sources

• Approaching the Thermodynamic Limit with Neural-Network Quantum States
• Solving the Hubbard model with Neural Quantum States
• Superconductivity in the two-dimensional Hubbard model revealed by neural quantum states
• Structure and dynamics of electron-phonon coupled systems using neural quantum states
• Quantum Spin Glass in the Two-Dimensional Disordered Heisenberg Model via Foundation Neural-Network Quantum States
• A Self-Attention Ansatz for Ab-initio Quantum Chemistry
• Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model
• Transformer-Based Neural Networks Backflow for Strongly Correlated Electronic Structure
• Fractionalized Fermi liquids and the cuprate phase diagram
• Small to large Fermi surface transition in a single band model, using randomly coupled ancillas
• Electronic spectra with paramagnon fractionalization in the single band Hubbard model
• Spin-Gap Proximity Effect Mechanism of High Temperature Superconductivity
• One-Dimensional Fermi liquids
• From the pseudogap metal to the Fermi liquid using ancilla qubits
• Deconfined criticality and ghost Fermi surfaces at the onset of antiferromagnetism in a metal
• Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons
• A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice
• Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor
• Quantum oscillations in the hole-doped cuprates and the confinement of spinons
• Thermal SU(2) lattice gauge theory for intertwined orders and hole pockets in the cuprates

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