Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap

Abstract

We propose a very accurate and efficient variational scheme for the ground state of the system of $p$-wave attractively interacting fermions confined in a one-dimensional harmonic trap. By the construction, the method takes the non-analytical part of interactions exactly into account and thus it approximates the true ground-state wave function in a whole range of interactions very accurately. Within the method, we determine different properties of the system for a different number of particles and different interactions. In this way, we explore how the system and its features transit from the ideal non-interacting Fermi gas to the system of infinitely strong attractions. Additionally, we demonstrate that the ansatz may also be used on a repulsive branch of interactions where other numerical methods break down. The presented method of including zero-range interactions is very universal and may be easily generalized to other one-dimensional confinements.

arXiv commentAuthors' version accepted for publication in New J. Phys

References in corpus (31)

• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• One-dimensional mixtures of several ultracold atoms: a review
• Theory of spinor Fermi and Bose gases in tight atom waveguides
• Two atoms in an anisotropic harmonic trap
• Effective interactions, Fermi-Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement
• Universal One-dimensional Atomic Gases Near Odd-wave Resonance
• Reentrant behavior of the breathing-mode-oscillation frequency in a one-dimensional Bose gas
• Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions
• Exact dynamics and decoherence of two cold bosons in a 1D harmonic trap
• Engineering quantum magnetism in one-dimensional trapped Fermi gases with p-wave interactions
• The fermionic limit of the delta-function Bose gas: a pseudopotential approach
• One-dimensional fermionic gases with attractive p-wave interaction in a hard-wall trap
• Tan's contact of a harmonically trapped one-dimensional Bose gas: strong-coupling expansion and conjectural approach at arbitrary interactions
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• One-dimensional multicomponent Fermi gas in a trap: quantum Monte Carlo study
• Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach
• Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Nanoplasmonic planar traps - a tool for engineering p-wave interactions
• Solvable Model of a Mixture of Bose-Einstein Condensates
• Discretized vs. continuous models of p-wave interacting fermions in 1D
• An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
• Pairing of a harmonically trapped fermionic Tonks-Girardeau gas
• Optimized Configuration Interaction Approach for Trapped Multiparticle Systems Interacting Via Contact Forces
• Two ultracold atoms in a completely anisotropic trap
• Variational approach for interacting ultra-cold atoms in arbitrary one-dimensional confinement
• Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many
• Breakdown of the scale invariance in the vicinity of Tonks-Girardeau gas
• Exactly solvable model of two interacting Rydberg-dressed atoms confined in a two-dimensional harmonic trap

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