Quasi-many-body localization of interacting fermions with long-range couplings

S. Thomson, M. Schirò
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引用次数: 14

Abstract

A number of experimental platforms for quantum simulations of disordered quantum matter, from dipolar systems to trapped ions, involve degrees of freedom which are coupled by power-law decaying hoppings or interactions, yet the interplay of disorder and interactions in these systems is far less understood than in their short-ranged counterpart. Here we consider a prototype model of interacting fermions with disordered long-ranged hoppings and interactions, and use the flow equation approach to map out its dynamical phase diagram as a function of hopping and interaction exponents. We demonstrate that the flow equation technique is ideally suited to problems involving long-range couplings due to its ability to accurately simulate very large system sizes. We show that, at large on-site disorder and for short-range interactions, a transition from a delocalized phase to a quasi many-body localized (MBL) phase exists as the hopping range is decreased. This quasi-MBL phase is characterized by intriguing properties such as a set of emergent conserved quantities which decay algebraically with distance. Surprisingly we find that a crossover between delocalized and quasi-MBL phases survives even in the presence of long-range interactions.
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远距离耦合费米子相互作用的准多体局域化
从偶极系统到捕获离子,许多无序量子物质的量子模拟实验平台涉及由幂律衰减跳跃或相互作用耦合的自由度,然而,这些系统中无序和相互作用的相互作用远不如它们的短程对应系统中理解得多。本文考虑了一个具有无序长程跳跃和相互作用的费米子相互作用的原型模型,并利用流动方程的方法绘制了其作为跳跃和相互作用指数函数的动态相图。我们证明,流动方程技术非常适合涉及远程耦合的问题,因为它能够准确地模拟非常大的系统尺寸。我们发现,在大的场域无序和短程相互作用下,随着跳变范围的减小,存在从离域相位到准多体局域相位的过渡。这种准mbl相具有有趣的特性,如一组随距离代数衰减的涌现守恒量。令人惊讶的是,我们发现即使在存在远程相互作用的情况下,离域相和准mbl相之间的交叉仍然存在。
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