Machine-learning approach to finite-size effects in systems with strongly interacting fermions

Abstract

We investigate the applicability of machine learning techniques in studying the finite-size effects associated with many-body physics. These techniques have an emerging presence in many-body theory as they have been used for interpolations, extrapolations, and in modeling wavefunctions. We will resolve several issues associated with machine learning and many-body calculations such as small datasets, outliers, and discontinuities, for the purpose of extrapolating finite calculations to macroscopic scales. We carry out a systematic investigation of two related systems by developing metrics that aim to avoid spurious effects and capture desired features. This work uses neural networks to extrapolate the Unitary Gas to the thermodynamic limit at zero-range, which is otherwise difficult to reach. The effective mass of strongly interacting neutron matter is also studied and makes use of the non-interacting problem to resolve discontinuous predictions. For this investigation, we also carried out new Auxiliary Field Diffusion Monte Carlo (AFDMC) calculations for a variety of densities and particle numbers. Ultimately, we demonstrate an effective utility for neural networks in this context.

10 pages, 9 figures; v2 corresponds to published version

References in corpus (16)

• Theory of ultracold Fermi gases
• Chiral effective field theory and nuclear forces
• Neutron matter at next-to-next-to-next-to-leading order in chiral effective field theory
• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Self-Learning Monte Carlo Method
• Accelerate Monte Carlo Simulations with Restricted Boltzmann Machines
• Quantum Monte Carlo calculation of the equation of state of neutron matter
• Thermodynamic Measurements in a Strongly Interacting Fermi Gas
• Finite-size correction in many-body electronic structure calculations
• Resonantly Interacting Fermions In a Box
• Correlated density-dependent chiral forces for infinite matter calculations within the Green's function approach
• BEC-BCS crossover and universal relations in unitary Fermi gases
• Quantum Monte Carlo approaches to nuclear and atomic physics
• Effective-Range Dependence of Resonantly Interacting Fermions
• Superfluid neutron matter with a twist
• Spin Susceptibility in Neutron Matter from Quantum Monte Carlo Calculations

Cited by in corpus (2)

• Multi-task learning on nuclear masses and separation energies with the kernel ridge regression
• Neural-Network Quantum States for Periodic Systems in Continuous Space