Abstract
We analyze the finite-size scaling of the average gap-ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin-chain with quasi-periodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of Berezinskii-Kosterlitz-Thouless (BKT) transition, the same as in the case of uniformly disordered systems as advocated in recent studies. Moreover, we observe that the critical disorder strength shows a clear sub-linear drift with the system-size as compared to the linear drift seen in random disordered models, suggesting that the finite-size effects in the MBL transition for the QP systems are less severe than that in the random disordered scenario. Moreover, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of on-site magnetizations that can be traced back to the strong correlations present in the QP potential.
Highlights
Generic isolated quantum many-body systems are expected, according to the eigenstate thermalization hypothesis [1,2,3], to approach equilibrium described by an appropriate statistical ensemble determined by a few global integrals of motion such as energy or total momentum – see [4, 5]
One exception to this hypothesis is provided by the phenomenon of many-body localization (MBL) [6, 7] which occurs in presence of strong disorder and interactions
We have performed a detailed analysis of the ergodic-MBL transition in finite-size quasi-periodic Heisenberg model
Summary
Generic isolated quantum many-body systems are expected, according to the eigenstate thermalization hypothesis [1,2,3], to approach equilibrium described by an appropriate statistical ensemble determined by a few global integrals of motion such as energy or total momentum – see [4, 5] One exception to this hypothesis is provided by the phenomenon of many-body localization (MBL) [6, 7] which occurs in presence of strong disorder and interactions. The average gap-ratio is equal to the random matrix theory (RMT) prediction r ≈ 0.531 in the fully delocalized regime of models preserving the generalized time reversal symmetry (the case we consider here), while for fully localized systems it takes the value characteristic for Poisson distribution r ≈ 0.386 [86]. As in the case for r, we average the rescaled EE over eigenstates corresponding to a particular disorder realization, and over different disorder realizations
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