Abstract
We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.
Highlights
The question of many-body localization (MBL) aims at extending the non-interacting Anderson localization problem [1] towards more realistic systems where interparticle interactions cannot be neglected
The ground state entanglement entropy grows logarithmically with subsystem size, with quasiperiodic oscillations [47]. We conclude this brief review of the free-fermions Fibonacci chain noting that the “structural” multifractality of the spectrum and single-particle states result in a power-law behavior for the thermodynamic [22,48,49] and transport [50,52] observables
Having established the existence of a many-body localization transition in the Fibonacci system, we investigate in more details the content of the thermal and localized phases
Summary
The question of many-body localization (MBL) aims at extending the non-interacting Anderson localization problem [1] towards more realistic systems where interparticle interactions cannot be neglected. The on-site potential terms hi are usually taken to be uncorrelated random variables drawn from a box distribution hi ∈ [−h, h], a binary distribution hi = ±h (+ with a probability p), or to be correlated variables, quasiperiodically varying according to the Aubry-André rule hAi A = h cos(2πωi + φ), where ω is an irrational frequency (φ a random phase) In all these cases, the model is known to undergo a many-body localization transition as h is increased [19, 32,33,34, 36, 37]. Multifractal, nature of its eigenstates and to the power-law behavior of its transport observables (discussed in Sec. 3), we can think of this model as following a line of metal-insulator transition points, as h is varied Can this model host an MBL phase when interactions are added?
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