Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study

Abstract

Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box. We use lattice Monte Carlo methods to determine essential quantities like the energy, which we compute as a function of coupling strength and particle number in the regime from few to many particles. Many-fermion systems bound by hard walls display non-trivial density profiles characterized by so-called Friedel oscillations (which are similar to those observed in harmonic traps). In non-interacting systems, the characteristic length scale of the oscillations is set by (2 kF)^(-1), where kF is the Fermi momentum, while repulsive interactions tend to generate Wigner-crystal oscillations of period (4 kF)^(-1). Based on the non-interacting result, we find a remarkably simple parametrization of the density profiles of the attractively interacting case, which we generalize to the one-body density matrix. While the total momentum is not a conserved quantity in the presence of hard walls, the magnitude of the momentum does provide a good quantum number. We are therefore able to provide a detailed characterization of the (quasi-)momentum distribution, which displays rather robust discontinuity at the Fermi surface. In addition, we determine the spatially varying on-site density-density correlation, which in turn yields Tan's contact density and, upon integration, Tan's contact. As is well known, the latter fully determines the short-range correlations and plays a crucial role in a multitude of equilibrium and non-equilibrium sum rules.

9 pages, 8 figures. Results unchanged; major improvements to text; new data on one-body density matrix, on-site correlations, and Tan's contact density with corresponding analysis

References in corpus (22)

• Many-Body Physics with Ultracold Gases
• Theory of ultracold Fermi gases
• Observation of chiral edge states with neutral fermions in synthetic Hall ribbons
• Visualizing edge states with an atomic Bose gas in the quantum Hall regime
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Ultracold Fermi Gases with Emergent SU(N) Symmetry
• Exact Relations for a Strongly-interacting Fermi Gas from the Operator Product Expansion
• Universal theory of nonlinear Luttinger liquids
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Virial theorems for trapped cold atoms
• Pairing in a system of a few attractive fermions in a harmonic trap
• Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
• Friedel Oscillations as a Probe of Fermionic Quasiparticles
• Pairing of few Fermi atoms in one dimension
• Quantum well states and amplified spin-dependent Friedel oscillations in thin films
• Few-fermion systems in one dimension: Ground- and excited-state energies and contacts
• Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo
• 2kF-Friedel to 4kF-Wigner oscillations in one-dimensional Fermi gases under confinement
• Friedel oscillations in one-dimensional metals: from Luttinger's theorem to the Luttinger liquid
• Slightly imbalanced system of a few attractive fermions in a one-dimensional harmonic trap
• Screening of a single impurity and Friedel oscillations in Fermi liquids
• Hard-Wall and Non-Uniform Lattice Monte Carlo Approaches to One-Dimensional Fermi Gases in a Harmonic Trap

Cited by in corpus (9)

• One-dimensional mixtures of several ultracold atoms: a review
• Evolution from few- to many-body physics in one-dimensional Fermi systems: One- and two-body density matrices, and particle-partition entanglement
• Universal Tan relations for quantum gases in one dimension
• Tan's contact and the phase distribution of repulsive Fermi gases: Insights from QCD noise analyses
• Intercomponent correlations in attractive one-dimensional mass-imbalanced few-body mixtures
• Vortices in low-density neutron matter and cold Fermi gases
• Detecting Friedel oscillations in ultracold Fermi gases
• Few-body perspective on fermionic pairing in one spatial dimension
• In-medium bound-state formation and inhomogeneous condensation in Fermi gases in a hard-wall box