Interaction-Driven Instabilities in the Random-Field XXZ Chain,Physical Review Letters

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Interaction-Driven Instabilities in the Random-Field XXZ Chain
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-09-12 , DOI: 10.1103/physrevlett.133.116502
Jeanne Colbois _{1,

2} , Fabien Alet _{1,

2} , Nicolas Laflorencie _{1,

2}

Affiliation

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 an ergodic instability, whereas at strong disorder the AL insulator directly turns into MBL, in agreement with a simple interpretation of the avalanche theory for restoration of ergodicity. We further map the phase diagram for the generic

X X Z

model in the disorder

h

–interaction

Δ

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 an inversion of orientation

ξ_{z} > ξ_{x}

. We find that the longitudinal length

ξ_{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.

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