Lattice methods for strongly interacting many-body systems

Abstract

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.

64 pages, 32 figures; topical review for J. Phys. G; replaced with published version

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Cited by in corpus (51)

• Two-particle multichannel systems in a finite volume with arbitrary spin
• Ab initio calculation of the spectrum and structure of ${}^{16}$O
• Multichannel one-to-two transition amplitudes in a finite volume
• Complex Langevin and other approaches to the sign problem in quantum many-body physics
• Pressure, compressibility, and contact of the two-dimensional attractive Fermi gas
• Phase structure of mass- and spin-imbalanced unitary Fermi gases
• Phase structure of spin-imbalanced unitary Fermi gases
• Precise determination of lattice phase shifts and mixing angles
• Quantum anomaly and thermodynamics of one-dimensional fermions with three-body interactions
• Finite-temperature equation of state of polarized fermions at unitarity
• Third-order perturbative lattice and complex Langevin analyses of the finite-temperature equation of state of non-relativistic fermions in one dimension
• Universality in one-dimensional fermions at finite temperature: Density, pressure, compressibility, and contact
• Inhomogeneous phases in one-dimensional mass- and spin-imbalanced Fermi gases
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
• Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
• Incorporating exact two-body propagators for zero-range interactions into $N$-body Monte Carlo simulations
• Zero-temperature equation of state of mass-imbalanced resonant Fermi gases
• Entanglement, noise, and the cumulant expansion
• Ground state of the two-dimensional attractive Fermi gas: essential properties from few- to many-body
• Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase
• Polarized fermions in one dimension: density and polarization from complex Langevin calculations, perturbation theory, and the virial expansion
• Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo
• Numerical study of the unitary Fermi gas across the superfluid transition
• Pairing patterns in one-dimensional spin- and mass-imbalanced Fermi gases
• The Tjon Band in Nuclear Lattice Effective Field Theory
• Solution to sign problems in models of interacting fermions and quantum spins
• Thermal equation of state of polarized fermions in one dimension via complex chemical potentials
• Virial coefficients of 1D and 2D Fermi gases by stochastic methods and a semiclassical lattice approximation
• Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps
• Lattice Effective Field Theory Simulations of Nuclei
• Second-Order Perturbation Theory in Continuum Quantum Monte Carlo Calculations
• Tan's contact and the phase distribution of repulsive Fermi gases: Insights from QCD noise analyses
• Leading- and next-to-leading order semiclassical approximation to the first seven virial coefficients of spin-1/2 fermions across spatial dimensions
• Few-body physics on a space-time lattice in the worldline approach
• Solution to the sign problem in a frustrated quantum impurity model
• Harmonically trapped fermions in two dimensions: ground-state energy and contact of SU(2) and SU(4) systems via nonuniform lattice Monte Carlo
• The entanglement spectrum and Rényi entropies of non-relativistic conformal fermions
• Solving reaction dynamics with quantum computing algorithms
• Third- and fourth-order virial coefficients of harmonically trapped fermions in a semiclassical approximation
• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Lattice methods and the nuclear few- and many-body problem
• Hard-Wall and Non-Uniform Lattice Monte Carlo Approaches to One-Dimensional Fermi Gases in a Harmonic Trap
• Quantum Many-Body Calculations using Body-Centered Cubic Lattices
• Multi-body wave function of ground and low-lying excited states using unornamented deep neural networks
• Convexity of the entanglement energy of SU($2N$)-symmetric fermions with attractive interactions
• Equation of state of non-relativistic matter from automated perturbation theory and complex Langevin
• Worldline Monte Carlo method for few body nuclear physics
• Lattice methods and effective field theory
• Particle Projection Using a Complex Langevin Method
• A lattice pairing-field approach to ultracold Fermi gases
• Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations