Journal Articles Phys.Rev.Lett. Year : 2024

Interaction-Driven Instabilities in the Random-Field XXZ Chain

Abstract

Despite enormous efforts devoted to the study of the many-body localization (MBL) phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a strong random magnetic field is lacking consensus. Here, we take a step back by exploring the weak interaction limit starting from the Anderson localized (AL) insulator. Through shift-invert diagonalization, we find that below a certain disorder threshold $h^*$, weak interactions necessarily lead to ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL. This agrees with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic XXZ model in the disorder $h$-- interaction $\Delta$ plane. Taking advantage of the total magnetization conservation, our results unveil the remarkable behavior of the spin-spin correlation functions: in the regime indicated as MBL by standard observables, their exponential decay undergoes a unique inversion of orientation $\xi_z>\xi_x$. We find that the longitudinal length $\xi_z$ is a key quantity for capturing ergodic instabilities, as it increases with system size near the thermal phase, in sharp contrast to its transverse counterpart $\xi_x$.

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hal-04522965 , version 1 (20-01-2025)

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Jeanne Colbois, Fabien Alet, Nicolas Laflorencie. Interaction-Driven Instabilities in the Random-Field XXZ Chain. Phys.Rev.Lett., 2024, 133 (11), pp.116502. ⟨10.1103/PhysRevLett.133.116502⟩. ⟨hal-04522965⟩
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