Transformer Wave Function for Quantum Long-Range models
arXiv:2407.04773 · doi:10.1103/PhysRevB.110.205147
Abstract
We employ a neural-network architecture based on the Vision Transformer (ViT) architecture to find the ground states of quantum long-range models, specifically the transverse-field Ising model for spin-1/2 chains across different interaction regimes. Harnessing the transformer's capacity to capture long-range correlations, we compute the full phase diagram and critical properties of the model, in both the ferromagnetic and antiferromagnetic cases. Our findings show that the ViT maintains high accuracy across the full phase diagram. We compare these results with previous numerical studies in the literature and, in particular, show that the ViT has a superior performance than a restricted-Boltzmann-machine-like ansatz.
14 pages, 7 figures, 2 tables
References in corpus (57)
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Entanglement entropy and conformal field theory
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- Quantum Entanglement in Neural Network States
- Long-range interacting quantum systems
- Dynamical crystallization in a low-dimensional Rydberg gas
- Direct measurement of the van der Waals interaction between two Rydberg atoms
- Entanglement entropy for the long range Ising chain
- Deep autoregressive models for the efficient variational simulation of many-body quantum systems
- Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
- Kitaev chains with long-range pairing
- Neural-Network Quantum States, String-Bond States, and Chiral Topological States
- Probing real-space and time resolved correlation functions with many-body Ramsey interferometry
- Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
- NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
- Solving the Bose-Hubbard model with machine learning
- Topological Massive Dirac Edge Modes and Long-Range Superconducting Hamiltonians
- Criticality and Phase Diagram of Quantum Long-Range models
- Green Function Monte Carlo with Stochastic Reconfiguration: an effective remedy for the sign problem disease
- Approximating strongly correlated spin and fermion wavefunctions with correlator product states
- Transformer variational wave functions for frustrated quantum spin systems
- Quantum-centric Supercomputing for Materials Science: A Perspective on Challenges and Future Directions
- Canonical solution of a system of long-range interacting rotators on a lattice
- Critical behavior of quantum magnets with long-range interactions in the thermodynamic limit
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Ground state approximation for strongly interacting systems in arbitrary dimension
- Variational Benchmarks for Quantum Many-Body Problems
- Fidelity and criticality of quantum Ising chain with long-range interactions
- Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
- Quasiparticles in quantum spin chains with long-range interactions
- Long range Coulomb interaction in bilayer graphene
- Area law of non-critical ground states in 1D long-range interacting systems
- Entanglement entropy in the Long-Range Kitaev chain
- Quantum-critical properties of the long-range transverse-field Ising model from quantum Monte Carlo simulations
- Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
- Edge states of the long-range Kitaev chain: an analytical study
- Analysis of the exactness of mean-field theory in long-range interacting systems
- Neural-network quantum states for many-body physics
- Finite-temperature critical behavior of long-range quantum Ising models
- Spreading of Correlations and Entanglement in the Long-Range Transverse Ising Chain
- Instability of the mean-field states and generalization of phase separation in long-range interacting systems
- Variational Monte Carlo with Large Patched Transformers
- Statistical Mechanics of systems with long range interactions
- Correlations, long-range entanglement and dynamics in long-range Kitaev chains
- Microcanonical Analysis of Exactness of the Mean-Field Theory in Long-Range Interacting Systems
- Equilibrium Properties of Quantum Spin Systems with Non-additive Long-Range Interactions
- Circuit Complexity through phase transitions: consequences in quantum state preparation
- Structural transitions of nearly second order in classical dipolar gases
- Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation
- Simplicity of mean-field theories in neural quantum states
- Neural-network quantum state study of the long-range antiferromagnetic Ising chain