标题： 衰落遍历性的标度理论 显示英文标题

标题： Scaling theory of fading ergodicity

摘要： 在大多数非相互作用的量子系统中，局域化标度理论预测在遍历和局域化区域中都存在单参数标度流。 另一方面，对于表现出多体遍历性破坏相变的相互作用系统，预期单参数标度假设会失效。 在这里，我们引入了一种渐隐遍历性的标度理论，这是多体遍历性破坏的前驱区域。 我们认为，双参数标度支配整个遍历区域；然而，(i) 它在遍历性破坏临界点处演化为单参数标度，临界指数为$\nu=1$，并且 (ii) 它在ETH点附近产生稳健的单参数标度。 我们的理论框架可能作为多体系统双参数标度理论的一个构建模块。 显示英文摘要

摘要： In most noninteracting quantum systems, the scaling theory of localization predicts one-parameter scaling flow in both ergodic and localized regimes. On the other hand, it is expected that the one-parameter scaling hypothesis breaks down for interacting systems that exhibit the many-body ergodicity breaking transition. Here we introduce a scaling theory of fading ergodicity, which is a precursor regime of many-body ergodicity breaking. We argue that the two-parameter scaling governs the entire ergodic regime; however, (i) it evolves into the one-parameter scaling at the ergodicity breaking critical point with the critical exponent $\nu=1$, and (ii) it gives rise to the resilient one-parameter scaling close to the ETH point. Our theoretical framework may serve as a building block for two-parameter scaling theories of many-body systems.