Perturbative quantum Monte Carlo method for nuclear physics

Abstract

While first order perturbation theory is routinely used in quantum Monte Carlo (QMC) calculations, higher-order terms present significant numerical challenges. We present a new approach for computing perturbative corrections in projection QMC calculations. We demonstrate the method by computing nuclear ground state energies up to second order for a realistic chiral interaction. We calculate the binding energies of several light nuclei up to ${}^{16}$O by expanding the Hamiltonian around the Wigner SU(4) limit and find good agreement with data. In contrast to the natural ordering of the perturbative series, we find remarkably large second order energy corrections. This occurs because the perturbing interactions break the symmetries of the unperturbed Hamiltonian. Our method is free from the sign problem and can be applied to QMC calculations for many-body systems in nuclear physics, condensed matter physics, ultracold atoms, and quantum chemistry.

5 pages main text, 6 pages supplemental material, more details on the perturbative expansion, version accepted for publication in Phys. Rev. Lett

References in corpus (10)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Structure and rotations of the Hoyle state
• Quantum Monte Carlo Simulations of the BCS-BEC Crossover at Finite Temperature
• Lattice Simulations for Light Nuclei: Chiral Effective Field Theory at Leading Order
• Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order
• ${}^{16}{\mathrm{O}}^{16}\mathrm{O}$ at RHIC and the LHC comparing $\alpha$ clustering vs substructure
• Chiral effective field theory on the lattice at next-to-leading order
• Three-nucleon bound states and the Wigner-SU(4) limit

Cited by in corpus (20)

• Wavefunction matching for solving quantum many-body problems
• Nuclear charge radii of silicon isotopes
• Ab initio study of the beryllium isotopes ${}^7$Be to ${}^{12}$Be
• Structure Factors for Hot Neutron Matter from Ab Initio Lattice Simulations with High-Fidelity Chiral Interactions
• Lattice Effective Field Theory Simulations of Nuclei
• Second-Order Perturbation Theory in Continuum Quantum Monte Carlo Calculations
• Binding of the three-hadron $D{D}^{\ast }K$ system from the lattice effective field theory
• Charged-particle bound states in periodic boxes
• Complex scaling in finite volume
• Sign-Problem-Free Nuclear Quantum Monte Carlo Simulation
• The triton lifetime from nuclear lattice effective field theory
• Perturbative treatment of nonlocal chiral interactions in auxiliary-field diffusion Monte Carlo calculations
• Charge-dependent nucleon-nucleon interaction at N${}^3$LO in nuclear lattice effective field theory
• Investigating nuclear beta decay using lattice quantum Monte Carlo approach
• Ab initio study of the radii of oxygen isotopes
• Worldline Monte Carlo method for few body nuclear physics
• Searching for the Tetraneutron Resonance on the Lattice
• Machine Learning Unveils the Power Law of Finite-Volume Energy Shifts
• Efficient emulation of nuclear ground states with neural-network variational Monte Carlo and eigenvector continuation
• Quantum State Preparation with Resolution Refinement