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# Quantum dynamics of disordered spin chains with power-law interactions

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### 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 ($$1/r^\alpha$$) 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 $$I(t)$$, growth of entanglement entropy $$S(t)$$, and growth of quantum Fisher information $$F_Q(t).$$ For sufficiently rapidly decaying interactions $$\alpha>\alpha_c$$ we find a many-body localized phase, in which $$I(t)$$ saturates to a non-zero value, entanglement entropy grows as $$S(t)\propto t^{1/\alpha}$$, 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 $$\alpha_c$$ is smaller for the XY model than for the Heisenberg model.

### Most cited references3

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### Fisher information and multiparticle entanglement

(2010)
The Fisher information $$F$$ gives a limit to the ultimate precision achievable in a phase estimation protocol. It has been shown recently that the Fisher information for a linear two-mode interferometer cannot exceed the number of particles if the input state is separable. As a direct consequence, with such input states the shot-noise limit is the ultimate limit of precision. In this work, we go a step further by deducing bounds on $$F$$ for several multiparticle entanglement classes. These bounds imply that genuine multiparticle entanglement is needed for reaching the highest sensitivities in quantum interferometry. We further compute similar bounds on the average Fisher information $$\bar F$$ for collective spin operators, where the average is performed over all possible spin directions. We show that these criteria detect different sets of states and illustrate their strengths by considering several examples, also using experimental data. In particular, the criterion based on $$\bar F$$ is able to detect certain bound entangled states.
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### Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter

(2017)
Cooling atoms to ultralow temperatures has produced a wealth of opportunities in fundamental physics, precision metrology, and quantum science. The more recent application of sophisticated cooling techniques to molecules, which has been more challenging to implement due to the complexity of molecular structures, has now opened door to the longstanding goal of precisely controlling molecular internal and external degrees of freedom and the resulting interaction processes. This line of research can leverage fundamental insights into how molecules interact and evolve to enable the control of reaction chemistry and the design and realization of a range of advanced quantum materials.
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### Exploring many-body localization and thermalization using semiclassical methods

(2017)
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### Author and article information

###### Journal
08 June 2018
###### Article
1806.03339