Evidence for unbounded growth of the number entropy in many-body localized phases

Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement

It is well known that in Anderson localized systems, starting from a random product state the entanglement entropy remains bounded at all times. However, we show that adding a single boundary term to an Anderson localized Hamiltonian leads to unbounded growth of entanglement. Our results imply that Anderson localization is not a local property. One cannot conclude that a subsystem has Anderson localized behavior without looking at the whole system, as a term that is arbitrarily far from the subsystem can affect the dynamics of the subsystem in such a way that the features of Anderson localizat…

Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential

In this work, we investigate the Anderson localization problems of the generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) with an unbounded quasi-periodic potential where the parameter $|α|\geq1$. The Lyapunov exponent $γ(E)$ and the mobility edges $E_c$ are exactly obtained for the unbounded quasi-periodic potential. With the Lyapunov exponent, we find that there exists a critical region in the parameter $λ-E$ plane. The critical region consists of critical states. In comparison with localized and extended states, the fluctuation of spatial extensions of the critical states is …

Unbounded growth of entanglement in models of many-body localization

An important and incompletely answered question is whether a closed quantum system of many interacting particles can be localized by disorder. The time evolution of simple (unentangled) initial states is studied numerically for a system of interacting spinless fermions in one dimension described by the random-field XXZ Hamiltonian. Interactions induce a dramatic change in the propagation of entanglement and a smaller change in the propagation of particles. For even weak interactions, when the system is thought to be in a many-body localized phase, entanglement shows neither localized nor diffu…

Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions

Power-law interactions play a key role in a large variety of physical systems. In the presence of disorder, these systems may undergo many-body localization for a sufficiently large disorder. Within the many-body localized phase the system presents in time an algebraic growth of entanglement entropy, $S_{vN}(t)\propto t^γ$. Whereas the critical disorder for many-body localization depends on the system parameters, we find by extensive numerical calculations that the exponent $γ$ acquires a universal value $γ_c\simeq 0.33$ at the many-body localization transition, for different lattice models an…

在具有准周期势的一维平带晶格中实现临界区域的提议

Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential

本文提出在含准周期势的一维平带晶格中实现 Ganeshan-Pixley-Das Sarma 模型的临界区域，并精确刻画迁移率边、Lyapunov 指数及不同转变附近的局域化长度临界指数。

具有无界势的光子晶格中光的离域化

Delocalization of light in photonic lattices with unbounded potentials

本文提出一类更广泛的无界势，无需准周期或特殊形状即可实现波离域化，并利用合成光子晶格中的光动力学为实验观测提供了可行平台。