Measuring Renyi Entropy in Neural Network Quantum States

TL;DR

This paper demonstrates how to compute Renyi entropy in neural network quantum states of a 1D quantum Ising model, revealing critical points, conformal behavior, and universal dynamical oscillations.

Contribution

It introduces a method to calculate Renyi entropy using neural network states and explores its behavior at criticality and during dynamical quenches.

Findings

Renyi entropy identifies the quantum critical point.

At criticality, entropy matches conformal field theory predictions.

Dynamical oscillations of entropy have universal frequencies.

Abstract

We compute the Renyi entropy in a one-dimensional transverse-field quantum Ising model by employing a swapping operator acting on the states which are prepared from the neural network methods. In the static ground state, Renyi entropy can uncover the critical point of the quantum phase transition from paramagnetic to ferromagnetic. At the critical point, the relation between the Renyi entropy and the subsystem size satisfies the predictions from conformal field theory. In the dynamical case, we find coherent oscillations of the Renyi entropy after the end of the linear quench. These oscillations have universal frequencies which may come from the superpositions of excited states. The asymptotic form of the Renyi entropy implies a new length scale away from the critical point. This length scale is also verified by the overlap of the reduced Renyi entropy against the dimensionless subsystem size.