HubbardNet: Efficient Predictions of the Bose-Hubbard Model Spectrum with Deep Neural Networks

TL;DR

HubbardNet employs deep neural networks to efficiently predict the energy spectrum and phase diagram of the Bose-Hubbard model, significantly reducing computational costs compared to traditional methods.

Contribution

The paper introduces HubbardNet, a DNN-based model that predicts the spectrum and phases of the Bose-Hubbard model from a single training, bypassing repeated Hamiltonian solutions.

Findings

Accurately predicts energy spectra as functions of U and N.

Identifies Mott insulator and superfluid phases.

Outperforms exact diagonalization in computational efficiency.

Abstract

We present a deep neural network (DNN)-based model (HubbardNet) to variationally find the ground state and excited state wavefunctions of the one-dimensional and two-dimensional Bose-Hubbard model. Using this model for a square lattice with $M$ sites, we obtain the energy spectrum as an analytical function of the on-site Coulomb repulsion, $U$, and the total number of particles, $N$, from a single training. This approach bypasses the need to solve a new hamiltonian for each different set of values $(U,N)$. Using \texttt{HubbardNet}, we identify the two ground state phases of the Bose-Hubbard model (Mott insulator and superfluid). We show that the DNN-parametrized solutions are in excellent agreement with results from the exact diagonalization of the hamiltonian, and it outperforms exact diagonalization in terms of computational scaling. These advantages suggest that our model is promising for efficient and accurate computation of exact phase diagrams of many-body lattice hamiltonians.