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A new approach for studying large numbers of fermions in the unitary regime

Jong-Wan Lee, David B. Kaplan, Michael G. Endres, Amy Nicholson

Published Jun 16, 2023• 0 citations
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Abstract

A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ0 = ≠/2. Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics. We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique. A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W. L.

DOI
10.17615/nv8x-xv76

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A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions. The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ0 = ≠/2. Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics. We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique. A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W. L.
A novel lattice approach is presented for studying systems comprising a large number of interacting nonrelativistic fermions.The construction is ideally suited for numerical study of fermions near unitarity-a strongly coupled regime corresponding to the two-particle s-wave scattering phase shift δ 0 = π/2.Such systems may be achieved experimentally with trapped atoms, and provide a starting point for an effective field theory description of nuclear physics.We discuss the construction of our lattice theory, which allows us to study systems of up to (but by no means limited to) 38 fermions with high accuracy and modest computational resources, and offer an overview of several applications of the technique.A more detailed discussion of applications and simulation results will be described in companion proceedings by A. N. N. and J-W.L.
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic few- and many-body systems, blurring the interfaces between condensed matter, atomic and low-energy nuclear physics. While some of these techniques have been in use in the area of condensed matter physics for a long time, others, such as hybrid Monte Carlo and improved effective actions, have only recently found their way across areas. With this topical review, we aim to provide a modest overview and a status update on a few notable recent developments. For the sake of brevity we focus on zero-temperature, non-relativistic problems. After a short introduction, we lay out some general considerations and proceed to discuss sampling algorithms, observables, and systematic effects. We show selected results on ground- and excited-state properties of fermions in the limit of unitarity. The appendix contains details on group theory on the lattice.
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic few- and many-body systems, blurring the interfaces between condensed matter, atomic and low-energy nuclear physics. While some of these techniques have been in use in the area of condensed matter physics for a long time, others, such as hybrid Monte Carlo and improved effective actions, have only recently found their way across areas. With this topical review, we aim to provide a modest overview and a status update on a few notable recent developments. For the sake of brevity we focus on zero-temperature, non-relativistic problems. After a short introduction, we lay out some general considerations and proceed to discuss sampling algorithms, observables, and systematic effects. We show selected results on ground- and excited-state properties of fermions in the limit of unitarity. The appendix contains details on group theory on the lattice.
We present a lattice study of up to N = 20 unitary fermions confined to a harmonic trap. Our preliminary results show better than 1% agreement with high precision solutions to the many-body Schrodinger equation for up to N = 6. We are able to make predictions for larger N which were inaccessible by the Hamiltonian approach due to computational limitations. Harmonic traps are used experimentally to study cold atoms tuned to a Feshbach resonance. We show that they also provide certain benefits to numerical studies of many-body correlators on the lattice. In particular, we anticipate that the methods described here could be used for studying nuclear physics.
A generic scenario of a crossover between weak-coupling and strong-coupling limits of a many-body quantum system is studied. Powerful numerical methods of investigating the strongly correlated regime are developed and applied to answering a number of important questions of the strongly correlated fermions physics. The internal structure of an exciton in an insulating medium is studied throughout the crossover between the (analytically solvable) strong- and weak-coupling limits. In the intermediate regime, accurate results for the exciton ground state are obtained and used to establish the limits of applicability of the corresponding limiting cases for the first time. A novel combination of the diagrammatic determinant Monte Carlo and the worm algorithm is developed and used for investigating the unitarity regime of the BEC-BCS crossover via simulating the dilute Fermi-Hubbard model. Superfluid phase transition and thermodynamic properties of the normal state are characterized for both lattice fermions and continuum unitary Fermi gas. The relation to current experiments with trapped ultracold quantum gases is discussed.
We present a lattice study of up to N = 20 unitary fermions confined to a harmonic trap.Our preliminary results show better than 1% agreement with high precision solutions to the many-body Schrodinger equation for up to N = 6.We are able to make predictions for larger N which were inaccessible by the Hamiltonian approach due to computational limitations.Harmonic traps are used experimentally to study cold atoms tuned to a Feshbach resonance.We show that they also provide certain benefits to numerical studies of many-body correlators on the lattice.In particular, we anticipate that the methods described here could be used for studying nuclear physicsThe