CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension

Abstract

We consider a one-dimensional system of particles with strong zero-range interactions. This system can be mapped onto a spin chain of the Heisenberg type with exchange coefficients that depend on the external trap. In this paper, we present an algorithm that can be used to compute these exchange coefficients. We introduce an open source code CONAN (Coefficients of One-dimensional N-Atom Networks) which is based on this algorithm. CONAN works with arbitrary external potentials and we have tested its reliability for system sizes up to around 35 particles. As illustrative examples, we consider a harmonic trap and a box trap with a superimposed asymmetric tilted potential. For these examples, the computation time typically scales with the number of particles as $O(N^{3.5\pm 0.4})$. Computation times are around 10 seconds for $N=10$ particles and less than 10 minutes for $N=20$ particles.

16 pages, 3 figures, 4 technical appendices, revised version with updated examples and appendices. Source code and compiled versions of CONAN can be found at http://phys.au.dk/forskning/forskningsomraader/amo/few-body-physics-in-a-many-body-world/conan

References in corpus (17)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• A one-dimensional liquid of fermions with tunable spin
• Two Fermions in a double well: Exploring a fundamental building block of the Hubbard model
• Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• Comparing and contrasting nuclei and cold atomic gases
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Exact solution for infinitely strongly interacting Fermi gases in tight waveguides
• Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Magnetism in strongly interacting one-dimensional quantum mixtures
• Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model
• Tunable self-assembled spin chains of strongly interacting cold atoms
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results

Cited by in corpus (23)

• One-dimensional mixtures of several ultracold atoms: a review
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
• Realizing time crystals in discrete quantum few-body systems
• Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
• Strongly Interacting One-Dimensional Systems with Small Mass Imbalance
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• Universal scaling of spin mixing dynamics in a strongly interacting one-dimensional Fermi gas
• Dynamics of spin and density fluctuations in strongly interacting few-body systems
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Dynamical realization of magnetic states in a strongly interacting Bose mixture
• Effects of interaction imbalance in a strongly repulsive one-dimensional Bose gas
• Mobile Spin Impurity in an Optical Lattice
• Spin Localization of a Fermi Polaron in a Quasirandom Optical Lattice
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Identical Wells, Symmetry Breaking, and the Near-Unitary Limit
• Emergence of junction dynamics in a strongly interacting Bose mixture
• One-Dimensional Quantum Systems - From Few to Many Particles
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Generation of spin currents by a temperature gradient in a two-terminal device