Neural network approach to quasiparticle dispersions in doped antiferromagnets

Abstract

Numerically simulating large, spinful, fermionic systems is of great interest in condensed matter physics. However, the exponential growth of the Hilbert space dimension with system size renders exact quantum state parameterizations impractical. Owing to their representative power, neural networks often allow to overcome this exponential scaling. Here, we investigate the ability of neural quantum states (NQS) to represent the bosonic and fermionic t − J model – the high interaction limit of the Hubbard model – on various 1D and 2D lattices. Using autoregressive, tensorized recurrent neural networks (RNNs), we study ground state representations upon hole doping the half-filled system. Additionally, we propose a method to calculate quasiparticle dispersions, applicable to any network architecture or lattice geometry, and allowing to infer the low-energy physics from NQS. By analyzing the strengths and weaknesses of the RNN ansatz we shed light on the challenges and promises of NQS for simulating bosonic and fermionic systems.