Accurate neural quantum states for interacting lattice bosons (2404.07869v2)

Abstract: In recent years, neural quantum states have emerged as a powerful variational approach, achieving state-of-the-art accuracy when representing the ground-state wave function of a great variety of quantum many-body systems, including spin lattices, interacting fermions or continuous-variable systems. However, accurate neural representations of the ground state of interacting bosons on a lattice have remained elusive. We introduce a neural backflow Jastrow Ansatz, in which occupation factors are dressed with translationally equivariant many-body features generated by a deep neural network. We show that this neural quantum state is able to faithfully represent the ground state of the 2D Bose-Hubbard Hamiltonian across all values of the interaction strength. We scale our simulations to lattices of dimension up to $20{\times}20$ while achieving the best variational energies reported for this model. This enables us to investigate the scaling of the entanglement entropy across the superfluid-to-Mott quantum phase transition, a quantity hard to extract with non-variational approaches.

• The paper introduces the neural backflow Jastrow Ansatz that accurately captures the ground state of interacting lattice bosons in the 2D Bose-Hubbard model.
• It combines backflow and Jastrow factors enhanced by deep neural network features to overcome the limitations of traditional simulation techniques.
• The Ansatz achieves variational V-scores as low as 2x10^-4, demonstrating exceptional scalability and precision across phase transitions.

Accurate Neural Quantum States for Interacting Lattice Bosons

The paper on "Accurate neural quantum states for interacting lattice bosons" presents a significant advancement in the representation of ground-state wave functions for lattice bosons using neural quantum states (NQS). The authors introduce a novel variational Ansatz, the neural backflow Jastrow Ansatz, which improves upon existing methods by accurately capturing the ground-state properties of the 2D Bose-Hubbard model across various interaction strengths.

The paper addresses the challenge of simulating interacting lattice bosons, a task complicated by the exponential growth of the Hilbert space with system size and particle number. Such systems are notoriously difficult to solve beyond mean-field approximations due to their complex quantum statistics. Previous methods like path-integral and quantum Monte Carlo techniques had limitations, particularly in directly accessing wave functions or suffering from the sign problem in certain scenarios.

The introduced neural backflow Jastrow Ansatz is a combination of backflow and Jastrow factors, where occupation factors are enriched with translationally equivariant many-body features generated by a deep neural network. This neural network effectively models complex many-body correlations, surpassing traditional Jastrow-type wave functions. The authors provide a robust analytical foundation for the structure and capabilities of the Ansatz, highlighting its ability to capture intricate correlations and phase transitions.

In their simulations, the authors demonstrate the capability of the neural backflow Jastrow Ansatz to represent the ground state of the 2D Bose-Hubbard Hamiltonian for lattices up to 20x20 in size, providing the best variational energies reported for this model. The paper benchmarks variational energies against Green-function Monte Carlo results, confirming the Ansatz's high accuracy with V-scores reaching as low as 2x10^-4. Notably, the approach scales efficiently, maintaining accuracy across multiple system sizes.

The paper's analytical and numerical sections reveal that the Ansatz can comprehensively account for Mott insulator and superfluid phases, including their transitions. Especially notable is the investigation of entanglement entropy scaling across the superfluid-to-Mott transition, aligning with theoretical predictions and offering insights into its critical behavior.

The theoretical and practical implications of this research are profound. The neural backflow Jastrow Ansatz provides a flexible and scalable tool for accurately modeling lattice bosonic systems, facilitating studies beyond the reach of current methods. This paves the way for applying NQS to complex bosonic lattices, potentially addressing the limitations posed by the sign problem in traditional quantum Monte Carlo simulations.

Future research can expand the applicability of this Ansatz to explore other quantum phenomena in lattice bosons, such as those subjected to synthetic magnetic fields or driven-dissipative dynamics. The flexibility and accuracy demonstrated by the neural Ansatz suggest significant potential for advancing our understanding of quantum many-body systems.