Comparing Symmetrized Determinant Neural Quantum States for the Hubbard Model

Abstract

Accurate simulations of the Hubbard model are crucial to understanding strongly correlated phenomena, where small energy differences between competing orders demand high numerical precision. In this work, Neural Quantum States are used to probe the strongly coupled and underdoped regime of the square-lattice Hubbard model. We systematically compare the Hidden Fermion Determinant State and the Jastrow-Backflow ansatz, parametrized by a Vision Transformer, finding that in practice, their accuracy is similar. We also test different symmetrization strategies, finding that output averaging yields the lowest energies, though it becomes costly for larger system sizes. On cylindrical systems, we consistently observe filled stripes. On the torus, our calculations display features consistent with a doped Mott insulator, including antiferromagnetic correlations and suppressed density fluctuations. Our results demonstrate both the promise and current challenges of neural quantum states for correlated fermions.

References in corpus (58)

• The density-matrix renormalization group in the age of matrix product states
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum Cluster Theories
• Spin Liquid State in an Organic Mott Insulator with Triangular Lattice
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Lattice symmetry breaking in cuprate superconductors: Stripes, nematics, and superconductivity
• The Hubbard Model
• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Polaron Problem by Diagrammatic Quantum Monte Carlo
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Wave function optimization in the variational Monte Carlo method
• Fermionic Projected Entangled Pair States
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Nickelate superconductors -- a renaissance of the one-band Hubbard model
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Quantum Monte Carlo study of the two-dimensional fermion Hubbard Model
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
• Diagrammatic Monte Carlo for Correlated Fermions
• Stripe order from the perspective of the Hubbard model
• Coexistence of superconductivity with partially filled stripes in the Hubbard model
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Quantum phase transition dynamics in the two-dimensional transverse-field Ising model
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Transformer variational wave functions for frustrated quantum spin systems
• Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices
• Empowering deep neural quantum states through efficient optimization
• Quantum-number projection in the path-integral renormalization group method
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Coupling quantum Monte Carlo and independent-particle calculations: self-consistent constraint for the sign problem based on density or density matrix
• Stripe and superconducting order competing in the Hubbard model on a square lattice studied by a combined variational Monte Carlo and tensor network method
• High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
• A simple linear algebra identity to optimize Large-Scale Neural Network Quantum States
• Optimizing Design Choices for Neural Quantum States
• Temperature Dependence of Spin and Charge Orders in the Doped Two-Dimensional Hubbard Model
• Neural-network quantum states for many-body physics
• Origin and fate of the pseudogap in the doped Hubbard model
• Variational Monte Carlo with Large Patched Transformers
• Metallic and insulating stripes and their relation with superconductivity in the doped Hubbard model
• Transformer Wave Function for two dimensional frustrated magnets: emergence of a Spin-Liquid Phase in the Shastry-Sutherland Model
• Ab-initio variational wave functions for the time-dependent many-electron Schrödinger equation
• Superfluid stiffness in cuprates: Effect of Mott transition and phase competition
• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Unifying view of fermionic neural network quantum states: From neural network backflow to hidden fermion determinant states
• Neural Projected Quantum Dynamics: a systematic study
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• Is attention all you need to solve the correlated electron problem?
• Comment on "Can Neural Quantum States Learn Volume-Law Ground States?"
• Are queries and keys always relevant? A case study on Transformer wave functions
• Spectroscopy of two-dimensional interacting lattice electrons using symmetry-aware neural backflow transformations
• Time-dependent Neural Galerkin Method for Quantum Dynamics
• Design principles of deep translationally-symmetric neural quantum states for frustrated magnets