Quantum dynamics of disordered spin chains with power-law interactions

Author
Abstract
We use extensive numerical simulations based on matrix product state methods to study the quantum dynamics of spin chains with strong on-site disorder and power-law decaying (1/r<sup>α</sup>) interactions. We focus on two spin-1/2 Hamiltonians featuring power-law interactions, Heisenberg and XY, and characterize their corresponding long-time dynamics using three distinct diagnostics: decay of a staggered magnetization pattern (t), growth of entanglement entropy S(t), and growth of quantum Fisher information F<sub>Q</sub>(t). For sufficiently rapidly decaying interactions α > α<sub>c</sub> we find a many-body localized phase, in which I(t) saturates to a nonzero value, entanglement entropy grows as S(t) ∝ t<sup>1/α</sup>, and Fisher information grows logarithmically. Importantly, entanglement entropy and Fisher information do not scale the same way (unlike short-range interacting models). The critical power α<sub>c</sub> is smaller for the <em>XY</em> model than for the Heisenberg model.
Year of Publication
2019
Journal
Physical Review A
Volume
99
Date Published
2019-03
ISSN Number
2469-9926
URL
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.99.033610
DOI
10.1103/PhysRevA.99.033610
JILA PI
Associated Institutes
Journal Article