Many-body localization enables iterative quantum optimization

We suggest an iterative quantum protocol, allowing to solve optimization problems with a glassy energy landscape. It is based on a periodic cycling around the tricritical point of the many-body localization transition. This ensures that each iteration leads to a non-exponentially small probability to find a lower local energy minimum. The other key ingredient is to tailor the cycle parameters to a currently achieved optimal state (the "reference" state) and to reset them once a deeper minimum is found. We show that, if the position of the tricritical point is known, the algorithm allows to approach the absolute minimum with any given precision in a polynomial time.

Non-Hermiticity-induced reentrant localization in a quasiperiodic lattice

In this paper, we demonstrate that the non-Hermiticity can induce reentrant localization in a generalized quasiperiodic lattice. Specifically, by considering a nonreciprocal dimerized lattice with staggered quasiperiodic disorder, we find that the localization transition can appear twice by increasing the disorder strength. We also unravel a multi-complex-real eigenenergy transition, whose transition points coincide with those in the localization phase transitions. Moreover, the impacts of boundary conditions on the localization properties have been clarified. Finally, we study the wavepacket dynamics in different parameter regimes, which offers an experimentally feasible route to detect the reentrant localization.

On intermediate statistics across many-body localization transition

The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian ensemble -- a single parameter model of level statistics proposed recently in the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa distribution is also} only slightly inferior to the two-parameter $\beta$-h ansatz shown {earlier} to reproduce {level statistics of} physical systems remarkably well.