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arXiv:2303.17381 · Physical review. B./Physical review. B

Exact dynamics of two holes in two-leg antiferromagnetic ladders

K. Knakkergaard Nielsen

Published Aug 18, 2023• 6 citations
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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, ${J}_{\ensuremath{\parallel}}$, and across, ${J}_{\ensuremath{\perp}}$, the ladder. We determine exact solutions for the low-energy one- and two-hole eigenstates. The presence of the trans-leg spin coupling, ${J}_{\ensuremath{\perp}}$, leads to a linear confining potential between the holes. As a result, holes on separate legs feature a superlinear binding energy scaling as ${({J}_{\ensuremath{\perp}}/t)}^{2/3}$ in the strongly correlated regime of ${J}_{\ensuremath{\perp}},{J}_{\ensuremath{\parallel}}\ensuremath{\le}t$. This behavior is linked to an emergent length scale $\ensuremath{\lambda}\ensuremath{\propto}{(t/{J}_{\ensuremath{\perp}})}^{1/3}$, stemming from the linear confining potential, and which describes how the size of the two-hole molecular state diverges for ${J}_{\ensuremath{\perp}},{J}_{\ensuremath{\parallel}}\ensuremath{\ll}t$. 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-neighbor 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, ${J}_{\ensuremath{\perp}},{J}_{\ensuremath{\parallel}}\ensuremath{\le}t$, we find this asymptotic distance to diverge as $t/{J}_{\ensuremath{\perp}}$, 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.

DOI
10.1103/physrevb.108.085125

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I unveil an emergent localization phenomenon pertaining to the motion of a dopant in a thermal spin lattice. This is rendered localized by thermal spin fluctuations, whereby it is in stark constrast to the intrinsic origin of Anderson localization for quenched disorder. The system of interest consists of spin- 1 / 2 particles organized in a two-leg ladder with nearest-neighbor Ising interactions J . The motion of a hole—the dopant—is initialized by suddenly removing a spin from the thermal spin ensemble, which then moves along the ladder via nearest-neighbor hopping t . I find that the hole remains for all values of J / t and for nonzero temperatures. The origin is an effective disorder potential seen by the hole and induced by thermal spin fluctuations. Its length scale is found to match with the underlying spin-spin correlation length at low temperatures. For ferromagnetic couplings ( J < 0 ), the associated localization length of the hole increases with decreasing temperature and becomes proportional to the correlation length at low temperatures, asymptotically delocalizing at low temperatures. For antiferromagnetic couplings ( J > 0 ), there is a smooth crossover between thermal localization at high temperatures to localization driven by the antiferromagnetic order at low temperatures. At infinite temperatures, the dynamics becomes independent of the sign of the spin coupling, whereby the localization length is a universal function of | J | / t , diverging as ( t / J ) 2 for | J | ≪ t . Finally, I analyze a setup with Rydberg-dressed atoms, which naturally realizes finite-range Ising interactions, accessible in current experimental setups. I show that the discovered localization phenomenon can be probed on experimentally accessible length- and timescales, providing a strong testing ground for my predictions. Published by the American Physical Society 2024
I demonstrate a pairing mechanism of dopants in a magnetic lattice, emerging from the underlying of the spins. The effect is demonstrated in a mixed-dimensional model, where dopants travel along a two-leg ladder, while the spins feature Ising interactions along the rungs and the legs of the ladder. The dynamics following the sudden immersion of two nearest neighbor dopants in an infinite temperature spin lattice shows that thermal spin disorder frustrates the relative motion of the dopants and enforces them to copropagate. The predictions are shown to be realistically testable in quantum simulation experiments.
We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. For the doped case, we find that static holes polarize their vicinity through a localization of singlets, reducing the frustration. This polarization induces short range repulsive forces between two holes and an oscillatory behavior of the long range two-hole energy. For most quantities investigated, we find very good agreement between the quantum dimer approach and the results from exact diagonalization.