Year: 2020
Type: article
Abstract: We develop a real-space renormalization-group (RSRG) scheme by appropriately inserting the long-range hopping t∼r^{-α} with nearest-neighbor interaction to study the entanglement entropy and maximum block size for the many-body localization (MBL) transition. We show that for α<2 there exists a localization transition with renormalized disorder that depends logarithmically on the finite size of the system. The transition observed for α>2 does not need a rescaling in disorder strength. Most important, we find that even though the MBL transition for α>2 falls in the same universality class as that of the short-range models, the transition for α<2 belongs to a different universality class. Because of the intrinsic nature of the RSRG flow toward delocalization, MBL phase for α>2 might suffer an instability in the thermodynamic limit while the underlying systems support algebraic localization. Moreover, we verify these findings by inserting microscopic details to the RSRG scheme where we additionally find a more appropriate rescaling function for disorder strength; we indeed uncover a power-law scaling with a logarithmic correction and a distinctly different stretched exponential scaling for α<2 and α>2, respectively, by analyzing system with finite size. This finding further suggests that microscopic RSRG scheme is able to give a hint of instability of the MBL phase for α>2 even considering systems of finite size.
Source: Physical review. E
Authors: Ranjan Modak, Tanay Nag
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2966422294