Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
arXiv:2407.05978 · doi:10.1103/PhysRevE.110.065305
Abstract
A continuous-time projection quantum Monte Carlo algorithm is employed to simulate the ground state of a short-range quantum spin-glass model, namely, the two-dimensional Edwards-Anderson Hamiltonian with transverse field, featuring Gaussian nearest-neighbor couplings. We numerically demonstrate that guiding wave functions based on self-learned neural networks suppress the population control bias below modest statistical uncertainties, at least up to a hundred spins. By projecting a two-fold replicated Hamiltonian, the spin overlap is determined. A finite-size scaling analysis is performed to estimate the critical transverse field where the spin-glass transition occurs, as well as the critical exponents of the correlation length and the spin-glass susceptibility. For the latter two, good agreement is found with recent estimates from the literature for different random couplings. We also address the spin-overlap distribution within the spin-glass phase, finding that, for the workable system sizes, it displays a non-trivial double-peak shape with large weight at zero overlap.
10 pages, 9 figures
References in corpus (48)
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
- Many-body localization in a quantum simulator with programmable random disorder
- Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
- Theory of Quantum Annealing of an Ising Spin Glass
- Perspectives of quantum annealing: Methods and implementations
- Many-Body Localization in a Quasiperiodic System
- Quantum critical dynamics in a 5000-qubit programmable spin glass
- NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
- Bose-Einstein Condensates in Optical Quasicrystal Lattices
- Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
- Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
- Towards the ground state of molecules via diffusion Monte Carlo on neural networks
- Population size bias in Diffusion Monte Carlo
- Transfer learning for scalability of neural-network quantum states
- Superglass phase of interaction-blockaded gases on a triangular lattice
- Emergent glassy behavior in a kagome Rydberg atom array
- Projective quantum Monte Carlo simulations guided by unrestricted neural network states
- Many Body Localization Due to Correlated Disorder in Fock Space
- Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing
- The Quantum Transition of the Two-Dimensional Ising Spin Glass: A Tale of Two Gaps
- Stability of the quantum Sherrington-Kirkpatrick spin glass model
- Quantum Monte Carlo Simulations of Tunneling in Quantum Adiabatic Optimization
- Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines
- Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo
- Existence of replica-symmetry breaking in quantum glasses
- A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
- Simulating disordered quantum systems via dense and sparse restricted Boltzmann machines
- Quasicrystalline Bose glass in the absence of disorder and quasidisorder
- Quantum annealing of an Ising spin-glass by Green's function Monte Carlo
- Classical-quantum crossover in the critical behavior of the transverse field S-K spin glass model
- Understanding Quantum Tunneling using Diffusion Monte Carlo Simulations
- Anomalous diffusion and localization in a positionally disordered quantum spin array
- jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration
- The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
- Ground state search by local and sequential updates of neural network quantum states
- Quantum slush state in Rydberg atom arrays
- A very fast inference algorithm for finite-dimensional spin glasses: Belief Propagation on the dual lattice
- Tunneling in projective quantum Monte Carlo simulations with guiding wave functions
- On the quantum spin glass transition on the Bethe lattice
- Localization of interacting Fermi gases in quasiperiodic potentials
- Amorphous quantum magnets in a two-dimensional Rydberg atom array
- Exact Solution for the Transverse Field Sherrington-Kirkpatrick Spin Glass Model with Continuous-Time Quantum Monte Carlo Method
- The QISG suite: high-performance codes for studying Quantum Ising Spin Glasses
- Supervised Training of Neural-Network Quantum States for the Next Nearest Neighbor Ising model
- Stochastic lists: Sampling multi-variable functions with population methods
- Quantum-critical properties of the one- and two-dimensional random transverse-field Ising model from large-scale quantum Monte Carlo simulations
- Primary and Secondary Order Parameters in the Fully Frustrated Transverse Field Ising Model on the Square Lattice