Spin transport in a tunable Heisenberg model realized with ultracold atoms (2005.09549v1)

Abstract: Simple models of interacting spins play an important role in physics. They capture the properties of many magnetic materials, but also extend to other systems, such as bosons and fermions in a lattice, systems with gauge fields, high-Tc superconductors, and systems with exotic particles such as anyons and Majorana fermions. In order to study and compare these models, a versatile platform is needed. Realizing such a system has been a long-standing goal in the field of ultracold atoms. So far, spin transport has only been studied in the isotropic Heisenberg model. Here we implement the Heisenberg XXZ model with adjustable anisotropy and use this system to study spin transport far from equilibrium after quantum quenches from imprinted spin helix patterns. In the non-interacting XX model, we find ballistic behavior of spin dynamics, while in the isotropic XXX model, we find diffusive behavior. For positive anisotropies, the dynamics ranges from anomalous super-diffusion to sub-diffusion depending on anisotropy, whereas for negative anisotropies, we observe a crossover in the time domain from ballistic to diffusive transport. This behavior contrasts with expectations for the linear response regime and raises new questions in understanding quantum many-body dynamics far away from equilibrium.

• The paper demonstrates that tuning the anisotropy in a spin-1/2 XXZ model with ultracold lithium atoms leads to clear transitions among ballistic, superdiffusive, and subdiffusive transport regimes.
• The experiment utilizes precise control of spin interactions through Feshbach resonances to simulate various quantum transport behaviors and validate theoretical predictions.
• The findings highlight the role of temporal crossovers and non-equilibrium dynamics, offering new insights into quantum many-body systems that challenge traditional integrability assumptions.

Examination of Spin Transport in a Tunable Heisenberg XXZ Model with Ultracold Atoms

This paper presents an exploration of spin transport in a highly controllable, tunable Heisenberg XXZ model, realized through ultracold atoms in optical lattices. The research primarily focuses on the quantum dynamics brought about by anisotropic interactions and analyzes the resultant transport phenomena in one-dimensional spin chains. Utilizing lithium atoms ($^7$Li), the authors implement a spin-1/2 XXZ model with adjustable anisotropy, examining transport behavior under varied non-equilibrium initial conditions, specifically quantum quenches of imprinted spin helix patterns.

Overview of Methodology

The research leverages the tunability of ultracold atomic systems to control spin interactions precisely by exploiting Feshbach resonances. The isotropic Heisenberg XXX model offers a baseline, wherein spin dynamics exhibit diffusive behavior. The transformation to the XXZ model allows the anisotropy parameter $\Delta$ to assume both positive and negative values, broadening the paper across different regimes of interaction. These regimes elucidate various transport phenomena: ballistic transport is evident in the non-interacting XX model, while the introduction of interactions transitions the system through superdiffusive, diffusive, and subdiffusive phases depending on the anisotropic parameter.

Significant Observations:

1. Ballistic Transport: In the XX (non-interacting) limit, spin waves display ballistic motion, with dynamics aligning closely to the Fermi velocity at half-filling. This regime is characterized by linear scaling of decay times with the inverse wave vector.
2. Diffusive Transport: The isotropic XXX model shows diffusive behavior, corroborated by a measured diffusion constant consistent with earlier findings in ferromagnetic systems. Here, interactions significantly slow transport processes.
3. Superdiffusion and Subdiffusion: For positive anisotropies, a progressive transition from ballistic to superdiffusive behavior is observed. The system's transport properties evolve smoothly, with exponents between 1 and 2 denoting a non-standard diffusion described by correlated steps or Lévy flights. In contrast, for $\Delta > 1$, the phases transition into subdiffusive behavior, suggesting transport through a medium affected by interactions akin to disorder but lacking it in essence.
4. Temporal Crossover: Negative anisotropies introduce a distinct initial ballistic phase followed by a transition to diffusive transport. This dual-phase decay emphasizes classical gas-like dynamics, wherein the initial regime is immune to negative interaction magnitudes, contrasting starkly with the positive anisotropic scenarios where interactions steadily influence from onset.

Implications and Future Directions

The implications of these findings extend to fundamental understandings of quantum many-body dynamics under non-equilibrium conditions. The discovery of varying diffusion regimes based on anisotropy presents avenues for further exploration into the role of quantum integrability and chaotic dynamics in determining transport properties. This research bridges discrepancies between theoretical expectations and observed dynamics, urging a deeper investigation into the crossover from ballistic to diffusive regimes and possibly new transport phenomena in quantum magnetic systems.

Future studies may expand on these results by incorporating effects that break integrability, such as next-nearest-neighbor interactions or higher dimensional lattice configurations. Experiments that manipulate initial conditions, introduce thermal effects, or extend evaluations to ferromagnetic domains promise to elucidate the quantum nature of transport further, providing insights into complex correlated systems, potentially mimicking conditions extant in high-$\mathbf{T}_c$ superconductors or novel quantum phases. The utilization of quantum simulators in this domain holds promise for comprehensive explorations into these challenging, yet fundamentally enriching domains of condensed matter physics.