Effect of long-range hopping and interactions on entanglement dynamics and many-body localization

Abstract

We numerically investigate the dynamics of entanglement in a chain of spinless fermions with nonrandom but long-range hopping and interactions, and with random on-site energies. For moderate disorder in the absence of interactions, the chain hosts delocalized states at the top of the band which undergo a delocalization-localization transition with increasing disorder. We find an interesting regime in this noninteracting disordered chain where the long-time entanglement entropy scales as $S(t)\sim \ln t$ and the saturated entanglement entropy scales with system size $L$ as $S(L,t\to \infty )\sim \ln L$. We further study the interplay of long-range hopping and interactions on the growth of entanglement and the many-body localization (MBL) transition in this system. We develop an analogy to higher-dimensional short-range systems to compare and contrast such behavior with the physics of MBL in a higher dimension.

12 pages, 9 figures; In the revised version, we have added an analogy between one-dimensional long-range and higher-dimensional short-range models in the context of many-body localization

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• Localization of interacting fermions at high temperature
• Exploring the many-body localization transition in two dimensions
• Many body localization in Heisenberg XXZ magnet in a random field
• Quantum quenches in 1+1 dimensional conformal field theories
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