Many-Body Neural Network Wavefunction for a Non-Hermitian Ising Chain

Abstract

Non-Hermitian (NH) quantum systems have emerged as a powerful framework for describing open quantum systems, non-equilibrium dynamics, and engineered quantum optical materials. However, solving the ground-state properties of NH systems is challenging due to the exponential scaling of the Hilbert space, and exotic phenomena such as the emergence of exceptional points. Another challenge arises from the limitations of traditional methods like exact diagonalization (ED). For the past decade, neural networks (NNs) have shown promise in approximating many-body wavefunctions, yet their application to NH systems remains largely unexplored. In this paper, we explore different NN architectures to investigate the ground-state properties of a parity-time-symmetric, one-dimensional NH, transverse field Ising model with a complex spectrum by employing a recurrent neural network (RNN), a restricted Boltzmann machine~(RBM), and a multilayer perceptron (MLP). We construct the NN-based many-body wavefunctions and validate our approach by recovering the ground-state properties of the model for small system sizes, finding excellent agreement with ED. Furthermore, for larger system sizes, we demonstrate that the RNN outperforms both the RBM and MLP. However, we show that the accuracy of the RBM and MLP can be significantly improved through transfer learning, allowing them to perform comparably to the RNN for larger system sizes. These results highlight the potential of neural network-based approaches--particularly for accurately capturing the low-energy physics of NH quantum systems in case of both weak and strong non-Hermiticity.

References in corpus (36)

• Machine learning and the physical sciences
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Non-Bloch Band Theory of Non-Hermitian Systems
• Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms
• Biorthogonal Quantum Mechanics
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Approximating quantum many-body wave-functions using artificial neural networks
• Symmetry and Higher-Order Exceptional Points
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Artificial Intelligence and Machine Learning for Quantum Technologies
• Machine Learning for Quantum Matter
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Systematics on ground-state energies of nuclei within the neural networks
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Transfer learning for scalability of neural-network quantum states
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Optimizing Design Choices for Neural Quantum States
• Exceptional points and the topology of quantum many-body spectra
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines
• The non-Hermitian skin effect: A perspective
• Symmetry-induced higher-order exceptional points in two dimensions
• Foundation Neural-Networks Quantum States as a Unified Ansatz for Multiple Hamiltonians
• Variational optimization of the amplitude of neural-network quantum many-body ground states
• Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains
• Many-body phase transitions in a non-Hermitian Ising chain
• Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
• Fine-tuning Neural Network Quantum States
• Autoregressive neural quantum states of Fermi Hubbard models
• Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice