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Many-body localization as a $d = infty$ Anderson localization with correlated disorder | | Hong-Ze Xu
; Shun-Yao Zhang
; Ze-Yu Rao
; Zhengwei Zhou
; Guang-Can Guo
; Ming Gong
; | | Date: |
15 Oct 2019 | | Abstract: | The disordered many-body systems can undergo a transition from the extended
ensemble to a localized ensemble, known as many-body localization (MBL), which
has been intensively explored in recent years. Nevertheless, the relation
between Anderson localization (AL) and MBL is still elusive. Here we show that
the MBL can be regarded as an infinite-dimensional AL with the correlated
disorder in a virtual lattice. We demonstrate this idea using the disordered
XXZ model, in which the excitation of $d$ spins over the fully polarized phase
can be regarded as a single-particle model in a $d$ dimensional virtual
lattice. With the increasing of $d$, the system will quickly approach the MBL
phase, in which the infinite-range correlated disorder ensures the saturation
of the critical disorder strength in the thermodynamic limit. From the
transition from AL to MBL, the entanglement entropy and the critical exponent
from energy level statics are shown to depend weakly on the dimension,
indicating that belonging to the same universal class. This work clarifies the
fundamental concept of MBL and presents a new picture for understanding the MBL
phase in terms of AL. | | Source: | arXiv, 1910.6601 | | Services: | Forum | Review | PDF | Favorites | |
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