利用张量网络研究相互作用费米子相变的 Lee-Yang 形式体系
Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
AI总结：
本文融合 Lee-Yang 相变理论与张量网络方法，通过有限尺寸费米子链序参量高阶累积量及矩生成函数零点外推，确定强排斥费米子的电荷密度波相界。
摘要：
预测相互作用量子多体系统的相图是凝聚态物理中的一个具有挑战性的问题。强相互作用和关联效应可能产生奇异物质状态，例如量子自旋液体和非常规超导体，这些状态通常会与包括有序磁体和电荷密度波在内的其他对称性破缺态相互竞争。本文提出了一种用于确定费米子系统相图的形式体系，它将相变相 Lee-Yang 理论领域的最新进展与多体张量网络方法相结合。利用这一策略，我们绘制了一条费米子链的相图，在该链中，强排斥作用导致电荷密度波形成。具体而言，我们从序参量的高阶累积量出发，提取有限尺寸链中矩生成函数的主导零点。通过将这些零点的位置外推至热力学极限，我们确定了相互竞争相之间的边界。我们的形式体系为确定费米子系统中的临界点提供了一种策略，并且该策略建立在序参量涨落的基础上，而这些涨落是可测量的物理量。
英文摘要：
Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and unconventional superconductors, that often compete with other symmetry broken states including ordered magnets and charge density waves. Here, we put forward a formalism for determining the phase diagram of fermionic systems that combines recent progress in the field of Lee-Yang theory of phase transitions with many-body tensor-network methods. Using this strategy, we map out the phase diagram of a fermionic chain, where charge density waves form owing to strong repulsion. Specifically, from the high cumulants of the order parameter, we extract the dominant zeros of the moment-generating function in chains of finite size. By extrapolating their positions to the thermodynamic limit, we determine the boundaries between competing phases. Our formalism provides a strategy for determining critical points in fermionic systems, and it is based on fluctuations of the order parameter, which are measurable quantities.
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