Discretized vs. continuous models of p-wave interacting fermions in 1D

Abstract

We present a general mapping between continuous and lattice models of Bose- and Fermi-gases in one dimension, interacting via local two-body interactions. For s-wave interacting bosons we arrive at the Bose-Hubbard model in the weakly interacting, low density regime. The dual problem of p-wave interacting fermions is mapped to the spin-1/2 XXZ model close to the critical point in the highly polarized regime. The mappings are shown to be optimal in the sense that they produce the least error possible for a given discretization length. As an application we examine the ground state of a interacting Fermi gas in a harmonic trap, calculating numerically real-space and momentum-space distributions as well as two-particle correlations. In the analytically known limits the convergence of the results of the lattice model to the continuous one is shown.

7 pages, 5 figures

References in corpus (18)

• The density-matrix renormalization group
• Efficient classical simulation of slightly entangled quantum computations
• Efficient simulation of one-dimensional quantum many-body systems
• Quantum Inverse Scattering Method and Correlation Functions
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• Realization of an Excited, Strongly-Correlated Quantum Gas Phase
• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• p-Wave Interactions in Low-Dimensional Fermionic gases
• Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials
• Theory of spinor Fermi and Bose gases in tight atom waveguides
• Exact numerical simulations of a one-dimensional, trapped Bose gas
• Bosonization, Pairing, and Superconductivity of the Fermionic Tonks-Girardeau Gas
• Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions
• Exact Solution for 1D Spin-Polarized Fermions with Resonant Interactions
• One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap
• Pairing of a harmonically trapped fermionic Tonks-Girardeau gas
• Stochastic Simulation of a finite-temperature one-dimensional Bose-Gas: from Bogoliubov to Tonks-Girardeau regime
• Ultracold bosons in disordered superlattices: Mott-insulators induced by tunneling

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• Quantum Shock Waves and Population Inversion in Collisions of Ultracold Atomic Clouds
• Spatio-temporal Fermionization of Strongly Interacting 1D Bosons
• Dynamics and evaporation of defects in Mott-insulating clusters of boson pairs
• Density profile of interacting Fermions in a one-dimensional optical trap
• Effective field theory of interactions on the lattice
• Efficient simulation of ultrafast quantum nonlinear optics with matrix product states
• Particle number conservation in quantum many-body simulations with matrix product operators
• Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap
• Ground-state properties of dilute spinless fermions in fractional dimensions
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