Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States

TL;DR

This paper introduces dilated RNN wave functions that incorporate long-range correlations efficiently, improving the modeling of quantum states with long-range dependencies while maintaining computational efficiency.

Contribution

The authors propose dilated RNN architectures that explicitly encode long-range correlations, outperforming standard RNNs and matching transformer capabilities with lower computational costs.

Findings

Dilated RNNs reproduce power-law correlations in the 1D transverse-field Ising model.

Dilated RNNs accurately model the long-range correlations of the 1D Cluster state.

Dilation changes correlation geometry, enabling better long-range dependency modeling.

Abstract

Neural Quantum States based on autoregressive recurrent neural network (RNN) wave functions enable efficient sampling without Markov-chain autocorrelation, but standard RNN architectures are biased toward finite-length correlations and can fail on states with long-range dependencies. A common response is to adopt transformer-style self-attention, but this typically comes with substantially higher computational and memory overhead. Here we introduce dilated RNN wave functions, where recurrent units access distant sites through dilated connections, injecting an explicit long-range inductive bias while retaining a favorable $\mathcal{O}(N \log N)$ forward pass scaling. We show analytically that dilation changes the correlation geometry and can induce power-law correlation scaling in a simplified linearized and perturbative setting. Numerically, for the critical 1D transverse-field Ising model, dilated RNNs reproduce the expected power-law connected two-point correlations in contrast to the exponential decay typical of conventional RNN ans\"atze. We further show that the dilated RNN accurately approximates the one-dimensional Cluster state, a paradigmatic example with long-range conditional correlations that has previously been reported to be challenging for RNN-based wave functions. These results highlight dilation as a simple geometric mechanism for building correlation-aware autoregressive neural quantum states.