Optimized Configuration Interaction Approach for Trapped Multiparticle Systems Interacting Via Contact Forces

Abstract

For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the eigenenergy of the desired level. It is shown that within the framework of this approach the well-converged results can be achieved at much smaller dimensions of the Hamiltonian matrix than with the standard approach that uses $\Omega =1$. We present calculations for model systems of identical bosons with harmonic and double-well potentials. Our results show promising potential for diminishing the computational cost of numerical simulations of various systems of trapped ultracold atoms.

arXiv comment4 pages, 3 fugures, Accepted by Physics Letters A

References in corpus (35)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Deterministic Preparation of a Tunable Few-Fermion System
• Fermionization of two distinguishable fermions
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Degenerate Bose-Bose mixture in a three-dimensional optical lattice
• Role of excited states in the splitting dynamics of interacting Bose-Einstein condensates when ramping-up a barrier
• Pairing in few-fermion systems with attractive interactions
• Few-boson dynamics in double wells: From single-atom to correlated-pair tunneling
• Entangling two transportable neutral atoms via local spin exchange
• Ground-state properties of few dipolar bosons in a quasi-one-dimensional harmonic trap
• Soluble Models of Strongly Interacting Ultracold Gas Mixtures in Tight Waveguides
• Non-Equilibrium Quantum Dynamics of Ultra-Cold Atomic Mixtures: the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons
• Few interacting fermions in one-dimensional harmonic trap
• Evolution from a Bose-Einstein condensate to a Tonks-Girardeau gas: An exact diagonalization study
• Composite fermionization of 1-D Bose-Bose mixtures
• Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture
• Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons
• Construction of analytical many body wave functions for correlated bosons in a harmonic trap
• Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
• Spectroscopy for a Few Atoms Harmonically-Trapped in One Dimension
• Two-component few-fermion mixtures in a one-dimensional trap: numerical versus analytical approach
• Boson Pairs in a One-dimensional Split Trap
• Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
• Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap
• Exactly solvable model of two trapped quantum particles interacting via finite-range soft-core interactions
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Numerically exact approach to few-body problems far from a perturbative regime
• Spectral properties and breathing dynamics of a few-body Bose-Bose mixture in a 1D harmonic trap
• Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• Mesoscopic superpositions of Tonks-Girardeau states and the Bose-Fermi mapping
• The optimized Rayleigh-Ritz scheme for determining the quantum-mechanical spectrum
• Correlation properties of a three-body bosonic mixture in a harmonic trap
• Low-energy excitations of a boson pair in a double-well trap
• Ground state properties of a Tonks-Girardeau Gas in a periodic potential

Cited by in corpus (13)

• One-dimensional mixtures of several ultracold atoms: a review
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
• Efficient construction of many-body Fock states having the lowest energies
• Reduced density matrix approach to ultracold few-fermion systems in one dimension
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• Variational approach for interacting ultra-cold atoms in arbitrary one-dimensional confinement
• Variational ansatz for $p$-wave fermions confined in a one-dimensional harmonic trap
• Comparison of renormalized interactions using one-dimensional few-body systems as a testbed
• Rabi-resonant behavior of periodically-driven correlated fermion systems
• Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential
• Few particles with an impurity in a one-dimensional harmonic trap
• Impurity immersed in a two-component few-fermion mixture in a one-dimensional harmonic trap