论文标题
在非弱点关键点处的非常规规模
Unconventional scaling at non-Hermitian critical points
论文作者
论文摘要
临界相转换包含各种深层物理,并通过缩放关系与热力学数量密切相关。然而,这些概念在非热性的背景下受到了挑战,在空间或时间差异会导致热力学极限不确定。在这项工作中,我们表明,在伪 - 温米顿人中仍然可以定义热力学的巨型潜力,并可以用来表征非温米特系统独有的批判性方面。以非热的Su-Schrieffer-Heeger(SSH)模型为范式示例,我们证明了复杂能量平面中拓扑相变的分数。当模型翻了一番和隐居时,这些分数订单加起来是隐居相变的整数订单。更令人叹为观止的是,保留高度退化的临界点的差距称为非Bloch带倒塌具有分数顺序,这些顺序不受常规缩放关系的限制,这是对皮肤模式积累的新兴额外长度尺度的证词。我们的工作展示了热力学方法可以证明在揭示非弱点关键点的非常规性能方面富有成果。
Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or temporal divergences render the thermodynamic limit ill-defined. In this work, we show that a thermodynamic grand potential can still be defined in pseudo-Hermitian Hamiltonians, and can be used to characterize aspects of criticality unique to non-Hermitian systems. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) model as a paradigmatic example, we demonstrate the fractional order of topological phase transitions in the complex energy plane. These fractional orders add up to the integer order expected of a Hermitian phase transition when the model is doubled and Hermitianized. More spectacularly, gap preserving highly degenerate critical points known as non-Bloch band collapses possess fractional order that are not constrained by conventional scaling relations, testimony to the emergent extra length scale from the skin mode accumulation. Our work showcases that a thermodynamic approach can prove fruitful in revealing unconventional properties of non-Hermitian critical points.