Ab Initio Study Defines Neutron and Fermi Polaron Equation of State on the Lattice

The behaviour of particles trapped within a sea of other particles, known as polarons, presents a fascinating challenge in both cold atomic physics and nuclear physics. Ryan Curry, Jasmine Kozar, and Alexandros Gezerlis, all from the University of Guelph, investigate this phenomenon using a sophisticated computational approach to model the interactions between a single impurity particle and a background of spin-polarized fermions. Their work establishes a robust method for studying polarons across a wide range of conditions, offering new insights into the equation of state for these complex systems. Crucially, the team’s calculations extend to the neutron polaron, a finding with important implications for understanding the fundamental properties of nuclear matter and providing stringent benchmarks for future theoretical and experimental investigations.

The approach is general, allowing for the study of the polaron across these regimes. Initially, the Fermi polaron at unitarity and for a wide range of scattering lengths is investigated, with comparisons made to previous theoretical and experimental studies. The neutron polaron is then explored, as it represents an important constraint for nuclear physics. A recently developed parametric matrix model emulates auxiliary-field quantum Monte Carlo (AFQMC) solutions to the two-body problem on the lattice, accelerating the tuning of lattice Hamiltonian parameters directly to two-body energies in a periodic box, following Lüscher’s formula.

Nuclear Matter Equation of State Calculations

This research focuses on understanding the fundamental properties of nuclear matter, the substance found within atomic nuclei and neutron stars. Scientists investigate many-body quantum systems, where numerous interacting particles create complex behaviours. A central goal is determining the equation of state (EoS) of nuclear matter, which describes the relationship between its pressure and density, crucial for modelling neutron stars and heavy-ion collisions. Observations of neutron stars, including their mass, radius, and tidal deformability, provide vital constraints on the EoS and reveal properties of nuclear matter at extreme densities.

Multi-messenger astronomy, combining gravitational wave and electromagnetic signals, is a key tool in this endeavour. The research also explores the fundamental forces between nucleons, protons and neutrons, using chiral effective field theory and related approaches. Scientists employ ab initio methods, solving the many-body Schrödinger equation directly from fundamental interactions, to achieve the most accurate results. Connections are drawn to research on ultracold atomic gases, which serve as a testbed for many-body physics and provide insights into nuclear systems. A range of computational methods are employed, including quantum Monte Carlo, auxiliary-field quantum Monte Carlo, coupled cluster theory, the no-core shell model, in-medium similarity renormalization group, path integral Monte Carlo, and density functional theory.

Specific research topics include constraining the nuclear EoS through analysis of neutron star observations and heavy-ion collisions, investigating three-nucleon interactions, studying few-body systems in both atomic gases and nuclei, and performing nuclear structure and reaction calculations. The symmetry energy, a key component of the EoS describing the energy cost of isospin asymmetry, is also investigated. Scientists quantify and address uncertainties in nuclear forces and many-body methods. This interdisciplinary research combines theoretical development, computational innovation, and experimental observations, particularly from astrophysics, to unravel the mysteries of nuclear matter and the fundamental forces that govern it.

AFQMC Reveals Polaron Properties Across Systems

Scientists have achieved a breakthrough in understanding the polaron, a quasiparticle formed when an impurity interacts with a sea of fermions, using the auxiliary-field quantum Monte Carlo (AFQMC) method on a lattice. This work investigates the polaron in both cold atomic and nuclear physics contexts, employing a single many-body Hamiltonian to demonstrate the versatility of their approach. The team’s calculations provide stringent benchmarks for future theoretical and experimental research in these diverse fields. The research centers on a lattice Hamiltonian, which incorporates both kinetic energy and an attractive interaction between particles.

The team successfully tuned the interaction strength and related parameters to accurately reproduce known scattering lengths for both cold atoms and neutron-neutron interactions, demonstrating precise control over the system’s properties. A novel method was developed to tune the lattice interaction, combining Lüscher’s formula for two particles in a finite volume with recently developed nuclear emulators. This allows for direct mapping of lattice Hamiltonian parameters to two-body energies in a periodic box, streamlining the process of accurately representing physical interactions. The team’s calculations at unitarity and across the BCS-BEC crossover demonstrate excellent agreement with existing experimental data and previous many-body calculations for cold atomic systems.

Furthermore, the team performed the first lattice calculations of the neutron polaron, providing an updated constraint over a range of Fermi momenta. These calculations demonstrate the ability of AFQMC to handle the fermion sign problem effectively and offer guidance for future experimental investigations in nuclear physics. The results confirm the power of AFQMC as a versatile and accurate method for studying many-body systems across diverse physical contexts, providing a foundation for further exploration of complex phenomena in both cold atomic and nuclear physics.

Auxiliary-Field Monte Carlo Validates Polaron Properties

Researchers have successfully applied the auxiliary-field Monte Carlo method to study the properties of a polaron, a quasiparticle formed when an impurity interacts with a surrounding sea of fermions, in both cold atomic physics and nuclear physics contexts. This work demonstrates the versatility of the method, allowing for the investigation of the polaron across a wide range of physical conditions and providing a benchmark for future theoretical and experimental studies. The team achieved excellent agreement with existing experimental and theoretical results, validating the accuracy of their approach. The calculations involved extrapolating results to more realistic conditions and exploring the use of computational emulators to refine the interactions within the model. While the polaron system presents computational challenges due to its inherent complexity, the constrained path auxiliary-field Monte Carlo method proved capable of delivering meaningful and accurate predictions. The authors suggest that these polaron calculations could serve as a foundation for investigating more complex nuclear phenomena, such as clustering or halo nuclei, and potentially constrain other theoretical calculations used in nuclear physics.