Neural network quantum states in the grand canonical ensemble

TL;DR

This paper introduces a neural quantum state architecture for bosonic systems in the grand canonical ensemble, enabling accurate predictions of physical observables with variable particle numbers.

Contribution

It presents a novel neural network-based approach to represent symmetric bosonic wavefunctions in Fock space, allowing study of systems with fluctuating particle numbers.

Findings

Achieved competitive variational energies in 1D and 2D bosonic systems.

Enabled estimation of condensate fractions and density profiles from first principles.

Demonstrated convergence to physical boson number under chemical potential.

Abstract

Variational Monte Carlo calculations have recently reached state-of-the-art accuracy in the approximation of ground state properties of quantum many-body systems. Making use of flexible neural quantum states and automatic differentiation has bypassed traditional computational obstacles such as reliance on basis sets. In this paper, we propose a neural quantum state architecture capable of representing symmetric bosonic wavefunctions in Fock space, enabling the study of systems with variable particle number. By supplementing our variational state with Monte Carlo sampling and geometric optimization, we demonstrate competitive variational energies across an array of one- and two-dimensional systems, converging to the physical boson number under a set chemical potential. Our approach enables accurate estimates of one-body reduced density matrices, opening access to observables such as condensate fractions and radial density profiles from first principles. Our method opens the door to numerical predictions of key measurable quantities in practical grand canonical systems.