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.
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.
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
The motion of dopants in magnetic spin lattices has received tremendous attention for at least four decades due to its connection to high-temperature superconductivity. Despite these efforts, we lack a complete understanding of their behavior, especially out of the equilibrium and at nonzero temperatures. In this paper, we take a significant step towards a much deeper understanding based on state-of-the-art matrix-product-state calculations. In particular, we investigate the nonequilibrium dynamics of a dopant in two-leg t − J ladders with antiferromagnetic XXZ spin interactions. In the Ising limit, we find that the dopant is for all investigated temperatures due to an emergent disordered potential, with a localization length controlled by the underlying correlation length of the spin lattice, which increases exponentially with decreasing temperature. The dopant, hereby, only delocalizes asymptotically in the zero temperature limit. This greatly generalizes the localization effect discovered recently in Hilbert space fragmented models [, ]. In the presence of spin-exchange processes at rate α , the dopant diffuses with a diffusion coefficient, D h , depending nonmonotonically on α . It initially increases linearly as D h ∝ α for α ≪ 1 before dropping off as α − 1 for α > 1 . Moreover, we show that the underlying spin dynamics at infinite temperature behaves qualitatively the same, albeit with important quantitative differences. We substantiate these findings by showing that the dynamics features self-similar scaling behavior, which strongly deviates from the Gaussian behavior of regular diffusion, especially for weak spin exchange. Finally, we show that the diffusion coefficient D h follows an Arrhenius relation at high temperatures, whereby it is exponentially suppressed upon cooling.
I investigate the motion of a single hole in 2D spin lattices with square and triangular geometries. While the spins have nearest neighbor Ising spin couplings J J , the hole is allowed to move only in 1D along a single line in the 2D lattice with nearest neighbor hopping amplitude t t . The non-equilibrium hole dynamics is initialized by suddenly removing a single spin from the thermal Ising spin lattice. I find that for any nonzero spin coupling and temperature, the hole is localized. This is an extension of the thermally induced localization phenomenon [Phys. Rev. Res. 6, 023325 (2024)] to the case, where there is a phase transition to a long-range ordered ferromagnetic phase. The dynamics depends only on the ratio of the temperature to the spin coupling, k_BT / |J| k B T / | J | , and on the ratio of the spin coupling to the hopping J/t J / t . I characterize these dependencies in great detail. In particular, I find universal behavior at high temperatures, common features for the square and triangular lattices across the Curie temperatures for ferromagnetic interactions, and highly distinct behaviors for the two geometries in the presence of antiferromagnetic interactions due geometric frustration in the triangular lattice.
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.
Abstract Conventional superconductivity emerges from pairing of charge carriers—electrons or holes—mediated by phonons 1 . In many unconventional superconductors, the pairing mechanism is conjectured to be mediated by magnetic correlations 2 , as captured by models of mobile charges in doped antiferromagnets 3 . However, a precise understanding of the underlying mechanism in real materials is still lacking and has been driving experimental and theoretical research for the past 40 years. Early theoretical studies predicted magnetic-mediated pairing of dopants in ladder systems 4–8 , in which idealized theoretical toy models explained how pairing can emerge despite repulsive interactions 9 . Here we experimentally observe this long-standing theoretical prediction, reporting hole pairing due to magnetic correlations in a quantum gas of ultracold atoms. By engineering doped antiferromagnetic ladders with mixed-dimensional couplings 10 , we suppress Pauli blocking of holes at short length scales. This results in a marked increase in binding energy and decrease in pair size, enabling us to observe pairs of holes predominantly occupying the same rung of the ladder. We find a hole–hole binding energy of the order of the superexchange energy and, upon increased doping, we observe spatial structures in the pair distribution, indicating repulsion between bound hole pairs. By engineering a configuration in which binding is strongly enhanced, we delineate a strategy to increase the critical temperature for superconductivity.
We study a mixed spin-(3/2, 1) ladder system with antiferromagnetic rung coupling and next-nearest-neighbor interaction. The exactly solved Ising-chain model is employed to investigate the ground-state properties and thermodynamics of the low-dimensional ladder system. Our results show that the competition between different exchange couplings brings in a large variety of ground states characterized by various values of normalized magnetization equal to 0, 1/5, 2/5, 3/5, 1. Moreover, an interesting double-peak structure is also detected in the thermal dependence of magnetic susceptibility and specific heat when the frustration comes into play. It is shown that the double-peak phenomenon at zero-field for the case of AF 2 ground-state arises from the very strong antiferromagnetic rung coupling, while other cases are attributed to the excitations induced by temperature and external field around the phase boundary.