Long-range interactions

Dimitri R. Yafaev

Zhen-Xia Niu, Wang, Qian

Long-range interacting quantum systems are useful for improving the performance of various applications of quantum technologies. In this work, we carry out a detailed analysis of how the long-range interaction affects the measurement precision in critical quantum metrology. By employing the paradigmatic model of a Kiteav chain with power-law decaying interaction, we focus on the impacts of long-range interaction on the critical sensing for the scenarios with and without uncertainty in system parameters.We show that the long-range interaction can be used as a valuable resource for enhancing the sensitivity of critical parameter estimation in both scenarios. Our findings not only provide more insights into the features of the long-range interacting systems, but also verify the usefulness of long-range interacting systems in quantum metrology.

Taro Nakada, Per Arne Rikvold, Takashi Mori +2 more

Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, we generally expect both long-range and short-range interactions to exist. In the short-range Ising model, the correlation length diverges at the critical point. In contrast, in the long-range interacting model the spin configuration is always uniform and the correlation length is zero. As long as a system has nonzero long-range interactions, it shows criticality in the mean-field universality class, and the spin configuration is uniform beyond a certain scale. Here we study the crossover from the pure short-range interacting model to the long-range interacting model. We investigate the infinite-range model (Husimi-Temperley model) as a prototype of this competition, and we study how the critical temperature changes as a function of the strength of the long-range interaction. This model can also be interpreted as an approximation for the Ising model on a small-world network. We derive a formula for the critical temperature as a function of the strength of the long-range interaction. We also propose a finite-size scaling form for the spin correlation length at the critical point, which is finite as long as the long-range interaction is included, though it diverges in the limit of the pure short-range model. These properties are confirmed by extensive Monte Carlo simulations.

Qian Wang

We examine a quantum heat engine with an interacting many-body working medium consisting of the long-range Kitaev chain to explore the role of long-range interactions in the performance of the quantum engine. By analytically studying two types of thermodynamic cycles, namely, the Otto cycle and Stirling cycle, we demonstrate that the work output and efficiency of a long-range interacting heat engine can be boosted by the long-range interactions, in comparison to the short-range counterpart. We further show that in the Otto cycle there exists an optimal condition for which the maximum enhancement in work output and efficiency can be achieved simultaneously by the long-range interactions. But, for the Stirling cycle, the condition which can give the maximum enhancement in work output does not lead to the maximum enhancement in efficiency. We also investigate how the parameter regimes under which the engine performance is enhanced by the long-range interactions evolve with a decrease in the range of interactions.

Shamik Gupta, Stefano Ruffo