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.

14 pages, 9 figures

References in corpus (13)

• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• One- and Two-Triplon Spectra of a Cuprate Ladder
• Transverse-Field Ising Dynamics in a Rydberg-Dressed Atomic Gas
• Competing magnetic orders in a bilayer Hubbard model with ultracold atoms
• Strong pairing in mixed dimensional bilayer antiferromagnetic Mott insulators
• Hole in the 2D Ising Antiferromagnet: Origin of the Incoherent Spectrum
• 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
• 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
• Omnipresent bound state of two holes in antiferromagnetic Bethe lattices

Cited by in corpus (5)

• Finite-Temperature Hole-Magnon Dynamics in an Antiferromagnet
• Thermally induced localization of dopants in a magnetic spin ladder
• Dopant pairing in a disordered magnetic spin ladder
• Beyond fragmented dopant dynamics in quantum spin lattices: Robust localization and non-Gaussian diffusion
• Localized dopant motion across the 2D Ising phase transition