Strongly interacting confined quantum systems in one dimension

Abstract

In one dimension, the study of magnetism dates back to the dawn of quantum mechanics when Bethe solved the famous Heisenberg model that describes quantum behaviour in magnetic systems. In the last decade, one-dimensional systems have become a forefront area of research driven by the realization of the Tonks-Girardeau gas using cold atomic gases. Here we prove that one-dimensional fermionic and bosonic systems with strong short-range interactions are solvable in arbitrary confining geometries by introducing a new energy-functional technique and obtaining the full spectrum of energies and eigenstates. As a first application, we calculate spatial correlations and show how both ferro- and anti-ferromagnetic states are present already for small system sizes that are prepared and studied in current experiments. Our work demonstrates the enormous potential for quantum manipulation of magnetic correlations at the microscopic scale.

11 pages, 2 figures, including methods, final version

References in corpus (7)

• From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
• Quantum magnetism without lattices in strongly interacting one-dimensional spinor 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
• Spectroscopy for a Few Atoms Harmonically-Trapped in One Dimension
• Fractional energy states of strongly-interacting bosons in one dimension

Cited by in corpus (149)

• Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap
• One-dimensional mixtures of several ultracold atoms: a review
• A unified ab-initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures
• Stable and charge-switchable quantum batteries
• Quantum spin transistor with a Heisenberg spin chain
• Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential
• Engineering the Dynamics of Effective Spin-Chain Models for Strongly Interacting Atomic Gases
• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• Strongly Interacting Quantum Gases in One-Dimensional Traps
• Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin
• Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension
• Quantum Impurity in a One-dimensional Trapped Bose Gas
• High-momentum tails as magnetic structure probes for strongly-correlated $SU(\kappa )$ fermionic mixtures in one-dimensional traps
• Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures
• Quantum magnetism in strongly interacting one-dimensional spinor Bose systems
• Magnetism in strongly interacting one-dimensional quantum mixtures
• Crossover between few and many fermions in a harmonic trap
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Two-flavor mixture of a few fermions of different mass in a one-dimensional harmonic trap
• Many interacting fermions in a one-dimensional harmonic trap: a quantum-chemical treatment
• Observation of pair tunneling and coherent destruction of tunneling in arrays of optical waveguides
• Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases
• Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides
• Phase Separation Dynamics Induced by an Interaction Quench of a Correlated Fermi-Fermi Mixture in a Double Well
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• Surmounting the sign problem in non-relativistic calculations: a case study with mass-imbalanced fermions
• One-dimensional Fermi gas with a single impurity in a harmonic trap: Perturbative description of the upper branch
• Few strongly interacting ultracold fermions in one-dimensional traps of different shapes
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• A variational approach to repulsively interacting three-fermion systems in a one-dimensional harmonic trap
• Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures
• Strongly interacting mesoscopic systems of anyons in one dimension
• Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: II. $N$ Particles
• Engineering quantum magnetism in one-dimensional trapped Fermi gases with p-wave interactions
• Exploring the few- to many-body crossover using cold atoms in one dimension
• SU(N) Fermions in a One-Dimensional Harmonic Trap
• Universal Tan relations for quantum gases in one dimension
• CONAN -- the cruncher of local exchange coefficients for strongly interacting confined systems in one dimension
• Quantum impurities: from mobile Josephson junctions to depletons
• Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
• Bose-Fermi Mapping and Multi-Branch Spin Chain Model for Strongly Interacting Quantum Gases in One-Dimension: Dynamics and Collective Excitations
• Coherent Oscillations in Small Fermi Polaron Systems
• Probing Ferromagnetic Order in Few-Fermion Correlated Spin-Flip Dynamics
• Four fermions in a one-dimensional harmonic trap: Accuracy of a variational-ansatz approach
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• Strongly interacting Bose-Fermi mixtures in one dimension
• Ultracold few fermionic atoms in needle-shaped double wells: spin chains and resonating spin clusters from microscopic Hamiltonians emulated via antiferromagnetic Heisenberg and t-J models
• Higher-order local and non-local correlations for 1D strongly interacting Bose gas
• Strongly correlated one-dimensional Bose-Fermi quantum mixtures: symmetry and correlations
• Strongly interacting one-dimensional quantum gas mixtures with weak p-wave interactions
• Realizing time crystals in discrete quantum few-body systems
• In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas
• Static and dynamic properties of a few spin $1/2$ interacting fermions trapped in an harmonic potential
• Energy, contact, and density profiles of one-dimensional fermions in a harmonic trap via non-uniform lattice Monte Carlo
• Analytical and numerical studies of Bose-Fermi mixtures in a one-dimensional harmonic trap
• Infinite Barriers and Symmetries for a Few Trapped Particles in One Dimension
• Strongly Interacting One-Dimensional Systems with Small Mass Imbalance
• Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps
• Simulation of Time-dependent Heisenberg Models in 1D
• Two interacting ultracold molecules in a one-dimensional harmonic trap
• An interpolatory ansatz captures the physics of one-dimensional confined Fermi systems
• Anomalous frequency shifts in a one-dimensional trapped Bose gas
• Universal scaling of spin mixing dynamics in a strongly interacting one-dimensional Fermi gas
• Dynamical Fermionization in One Dimensional Spinor Gases
• Exact ordering of energy levels for one-dimensional interacting Fermi gases with $SU(n)$ symmetry
• Reduced density matrix approach to ultracold few-fermion systems in one dimension
• One-Body Density Matrix and Momentum Distribution of Strongly Interacting One-Dimensional Spinor Quantum Gases
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• Two-point momentum correlations of few ultracold quasi-one-dimensional trapped fermions: Diffraction patterns
• Parity effect in a mesoscopic Fermi gas
• Repulsive Fermi polarons with negative effective mass
• Comparing models for the ground state energy of a trapped one-dimensional Fermi gas with a single impurity
• Dynamical fermionization in a one-dimensional Bose-Fermi mixture
• Self-consistent determination of the many-body state of ultracold bosonic atoms in a one-dimensional harmonic trap
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• Interplay of phase separation and itinerant magnetism for correlated few fermions in a double-well
• Tan's contact scaling behaviour for trapped Lieb-Liniger bosons: from two to many
• Hyperspherical Treatment of Strongly-Interacting Few-Fermion Systems in One Dimension
• Ground-state energy, density profiles, and momentum distribution of attractively interacting 1D Fermi gases with hard-wall boundaries: a Monte Carlo study
• Engineering entanglement Hamiltonians with strongly interacting cold atoms in optical traps
• Many-body density and coherence of trapped cold bosons
• Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement
• Mass-imbalance induced structures of binary atomic mixtures in box potentials
• Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry
• Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gas: Spin-dependent properties
• Spin-incoherent Luttinger liquid of one-dimensional SU($\kappa$) fermions
• Dynamical realization of magnetic states in a strongly interacting Bose mixture
• One-dimensional Repulsive Fermi Gas in a Tunable Periodic Potential
• Spin-incoherent one-dimensional spin-1 Bose Luttinger liquid
• Tuning an effective spin chain of three strongly interacting one-dimensional fermions with the transversal confinement
• Finite temperature contact for SU(2) fermions trapped in a 1D harmonic confinement
• Effects of interaction imbalance in a strongly repulsive one-dimensional Bose gas
• On pairs of interacting electrons in a quantum wire
• Quench dynamics of dipolar fermions in a one-dimensional harmonic trap
• Universal low energy physics in one-dimensional multicompnent Fermi gases with a strongly repulsive $\delta$-function interaction
• Symmetry oscillations in strongly interacting one-dimensional mixtures
• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Ultrastable super-Tonks-Girardeau gases under weak dipolar interactions
• Spin Localization of a Fermi Polaron in a Quasirandom Optical Lattice
• Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Mobile Spin Impurity in an Optical Lattice
• Exact closed-form analytic wave functions in two dimensions: Contact-interacting fermionic spinful ultracold atoms in a rapidly rotating trap
• A generalized effective spin-chain formalism for strongly interacting spinor gases in optical lattice
• Identical Wells, Symmetry Breaking, and the Near-Unitary Limit
• Are smooth pseudopotentials a good choice for representing short-range interactions?
• Dynamics of small trapped one-dimensional Fermi gas under oscillating magnetic fields
• Repulsive dynamics of strongly attractive one-dimensional quantum gases
• Persistent currents in a strongly interacting multicomponent Bose gas on a ring
• Experimentally accessible invariants encoded in interparticle correlations of harmonically trapped ultra-cold few-fermion mixtures
• Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture
• Emergence of junction dynamics in a strongly interacting Bose mixture
• Symmetries and Correlations in Strongly Interacting One-dimensional Quantum Gases
• Dynamical fermionization in one-dimensional spinor gases at finite temperature
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• State transfer in an inhomogeneous spin chain
• Two ultracold highly magnetic atoms in a one-dimensional harmonic trap
• Generalized Bose-Fermi mapping and strong coupling ansatz wavefunction for one dimensional strongly interacting spinor quantum gases
• Trap effects and continuum limit of the Hubbard model in the presence of a harmonic potential
• Interaction-induced Bloch Oscillation in a Harmonically Trapped and Fermionized Quantum Gas in One Dimension
• Itinerant ferromagnetism in the repulsive Hubbard chain with anisotropic odd-wave attraction
• A universal graph description for one-dimensional exchange models
• Local manipulation of quantum magnetism in 1D ultracold Fermi gases across narrow resonances
• A Solvable Model for Decoupling of Interacting Clusters
• Spin-charge correlations in finite one-dimensional multi-band Fermi systems
• Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
• Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
• Dynamical probing of high-order spin coherence in one-dimensional mixtures
• One-Dimensional Quantum Systems - From Few to Many Particles
• EPR pairing dynamics in Hubbard model with resonant $U$
• Shortcut to spin dynamics for quantum mixtures
• Numerical methods and analytic results for one-dimensional strongly interacting spinor gases
• Exact Solution for Two $\delta$-Interacting Bosons on a Ring in the Presence of a $\delta$-Barrier: Asymmetric Bethe Ansatz for Spatially Odd States
• Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss
• Manifold formation and crossings of ultracold lattice spinor atoms in the intermediate interaction regime
• From few to many body degrees of freedom
• Five is More: Comments on Symmetry, Integrability, and Solvability for a Few Particles in a One-Dimensional Trap
• Strongly Repulsive 1D Gases at Higher Branches: Spin-Charge Correlation and Coupled Spin-Chain Model
• Several fermions strongly interacting with a heavy mobile impurity in a one-dimensional harmonic trap
• Composite Bosons Superposition Ansatz Approach to One-Dimensional Trapped Few-Fermion Systems
• Generation of spin currents by a temperature gradient in a two-terminal device
• Symmetry oscillations sensitivity to SU(2)-symmetry breaking in quantum mixtures
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Impenetrability in Floquet scattering in one dimension
• Efficient determination of eigenenergies and eigenstates of $N$ ($N=3$--$4$) identical 1D bosons and fermions under external harmonic confinement
• Systematic interpolatory ansatz for one-dimensional polaron systems