Exact dynamics of two holes in two-leg antiferromagnetic ladders

Abstract

We study the motion of holes in a mixed-dimensional setup of an antiferromagnetic ladder, featuring nearest neighbor hopping $t$ along the ladders and Ising-type spin interactions along, $J_{\parallel }$, and across, $J_{\perp }$, the ladder. We determine exact solutions for the low-energy one- and two-hole eigenstates. The presence of the trans-leg spin coupling, $J_{\perp }$, leads to a linear confining potential between the holes. As a result, holes on separate legs feature a super-linear binding energy scaling as $(J_{\perp }/t{)}^{2/3}$ in the strongly correlated regime of $J_{\perp },J_{\parallel }\le t$. This behavior is linked to an emergent length scale $\lambda \propto (t/J_{\perp }{)}^{1/3}$, stemming from the linear confining potential, and which describes how the size of the two-hole molecular state diverges for $J_{\perp },J_{\parallel }\ll t$. On the contrary, holes on the same leg unbind at sufficiently low spin couplings. This is a consequence of the altered short-range boundary condition for holes on the same leg, yielding an effective Pauli repulsion between them, limiting their kinetic energy and making binding unfavorable. Finally, we determine the exact nonequilibrium quench dynamics following the sudden immersion of initially localized nearest neigbhor holes. The dynamics is characterized by a crossover from an initial ballistic quantum walk to an aperiodic oscillatory motion around a finite average distance between the holes due to the confining potential between them. In the strongly correlated regime of low spin couplings, $J_{\perp },J_{\parallel }\le t$, we find this asymptotic distance to diverge as $t/J_{\perp }$, showing a much stronger scaling than the eigenstates. The predicted results should be amenable to state-of-the-art quantum simulation experiments using currently implemented experimental techniques.

arXiv comment14 pages, 9 figures

References in corpus (56)

• Correlated Electrons in High Temperature Superconductors
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Fermi-Hubbard physics with atoms in an optical lattice
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Spin and Charge Resolved Quantum Gas Microscopy of Antiferromagnetic Order in Hubbard Chains
• Many-body interferometry of a Rydberg-dressed spin lattice
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Tunable Superfluidity and Quantum Magnetism with Ultracold Polar Molecules
• Bad metallic transport in a cold atom Fermi-Hubbard system
• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Revealing Hidden Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators
• Stripes in the two-dimensional t-J model with infinite projected entangled-pair states
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• Order-Disorder Transition in a Two-Layer Quantum Antiferromagnet
• Imaging magnetic polarons in the doped Fermi-Hubbard model
• The Spin Dynamics of the Spin Ladder, Dimer Chain Material Sr14Cu24O41
• String patterns in the doped Hubbard model
• Observation of canted antiferromagnetism with ultracold fermions in an optical lattice
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Quantum magnetism and topological ordering via enhanced Rydberg-dressing near Förster-resonances
• Confinement of fractional quantum number particles in a condensed matter system
• Time-Resolved Observation of Spin-Charge Deconfinement in Fermionic Hubbard Chains
• One- and Two-Triplon Spectra of a Cuprate Ladder
• Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas
• Quantum state engineering of a Hubbard system with ultracold fermions
• Collective spin excitations in a quantum spin ladder probed by high-resolution Resonant Inelastic X-ray Scattering
• Competing magnetic orders in a bilayer Hubbard model with ultracold atoms
• Doublon-hole correlations and fluctuation thermometry in a Fermi-Hubbard gas
• Quench Dynamics of a Fermi Gas with Strong Non-Local Interactions
• Phase Transition, Longitudinal Spin Fluctuations and Scaling in a Two-Layer Antiferromagnet
• Parton theory of magnetic polarons: Mesonic resonances and signatures in dynamics
• Coupling a mobile hole to an antiferromagnetic spin background: Transient dynamics of a magnetic polaron
• Direct observation of multi-spinon excitations outside of the two-spinon continuum in the antiferromagnetic spin chain cuprate Sr2CuO3
• Holes in the t-J_z model: a thorough study
• Angle-resolved photoemission spectroscopy with quantum gas microscopes
• Angle-resolved photoemission spectroscopy of a Fermi-Hubbard system
• Strong pairing in mixed dimensional bilayer antiferromagnetic Mott insulators
• A comprehensive numerical and analytical study of two holes doped into the 2D t-J model
• Quantum-Critical Behavior in a Two-Layer Antiferromagnet
• A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model
• Meson formation in mixed-dimensional t-J models
• Bound states of holes in an antiferromagnet
• Dynamical formation of a magnetic polaron in a two-dimensional quantum antiferromagnet
• Quantum Many-Body Simulations of the 2D Fermi-Hubbard Model in Ultracold Optical Lattices
• Hole in the 2D Ising Antiferromagnet: Origin of the Incoherent Spectrum
• Studies of one- and two-hole states in the 2D t-J model via series expansions
• Z2 parton phases in the mixed-dimensional $t-J_z$ model
• Nonequilibrium Hole Dynamics in Antiferromagnets: Damped Strings and Polarons
• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Theoretical study of the spin and charge dynamics of two-leg ladders as probed by resonant inelastic x-ray scattering
• Low energy and dynamical properties of a single hole in the t-Jz model
• Dynamical signatures of thermal spin-charge deconfinement in the doped Ising model
• Two holes in a two-dimensional quantum antiferromagnet: A variational study based on entangled-plaquette states
• Two holes in the t-J model form a bound state for any nonzero J/t
• Omnipresent bound state of two holes in antiferromagnetic Bethe lattices

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• Localized dopant motion across the 2D Ising phase transition