Calculating Renyi Entropies with Neural Autoregressive Quantum States

Abstract

Entanglement entropy is an essential metric for characterizing quantum many-body systems, but its numerical evaluation for neural network representations of quantum states has so far been inefficient and demonstrated only for the restricted Boltzmann machine architecture. Here, we estimate generalized Renyi entropies of autoregressive neural quantum states with up to N=256 spins using quantum Monte Carlo methods. A naive "direct sampling" approach performs well for low-order Renyi entropies but fails for larger orders when benchmarked on a 1D Heisenberg model. We therefore propose an improved "conditional sampling" method exploiting the autoregressive structure of the network ansatz, which outperforms direct sampling and facilitates calculations of higher-order Renyi entropies in both 1D and 2D Heisenberg models. Access to higher-order Renyi entropies allows for an approximation of the von Neumann entropy as well as extraction of the single copy entanglement. Both methods elucidate the potential of neural network quantum states in quantum Monte Carlo studies of entanglement entropy for many-body systems.

References in corpus (8)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Entanglement spectrum in one-dimensional systems
• MADE: Masked Autoencoder for Distribution Estimation
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Constructing neural stationary states for open quantum many-body systems
• Entanglement entropy of critical spin liquids
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo

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• Infinite Neural Network Quantum States: Entanglement and Training Dynamics
• Sparse Autoregressive Neural Networks for Classical Spin Systems
• Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Transmission of coherent information at the onset of interactions
• Topological Order in Neural Wavefunctions