论文标题
关键性地关联非热和遗传学量子系统
Relating non-Hermitian and Hermitian quantum systems at criticality
论文作者
论文摘要
我们演示了三种类型的转换，这些转换在临界时建立了遗产和非列米特量子系统之间的联系，可以通过共形场理论（CFTS）来描述。对于保留能量和纠缠光谱的转换，从纠缠熵的对数缩放率获得的相应中心电荷对于赫尔米尼和非弱者系统都是相同的。在保留能量谱的同时，第二个变换并不能坚持纠缠频谱。这导致了不同的纠缠熵量表，并为两种类型的系统产生了不同的中央电荷。我们使用应用于自由费用情况的扩张方法证明了这种转变。通过这种方法，我们表明，具有中央电荷$ C = -4 $的非热门系统可以映射到中央电荷$ C = 2 $的Hermitian系统。最后，我们使用参数$ ϕ \ to -1/ϕ $研究了斐波那契模型中的Galois共轭，其中转换不能同时保留能量和纠缠光谱。我们演示了斐波那契模型及其GALOIS共轭相关的三级ising模型/3状态POTTS模型和Lee-Yang模型，其中具有纠缠熵缩放特性的负中央电荷。
We demonstrate three types of transformations that establish connections between Hermitian and non-Hermitian quantum systems at criticality, which can be described by conformal field theories (CFTs). For the transformation preserving both the energy and the entanglement spectra, the corresponding central charges obtained from the logarithmic scaling of the entanglement entropy are identical for both Hermitian and non-Hermitian systems. The second transformation, while preserving the energy spectrum, does not perserve the entanglement spectrum. This leads to different entanglement entropy scalings and results in different central charges for the two types of systems. We demonstrate this transformation using the dilation method applied to the free fermion case. Through this method, we show that a non-Hermitian system with central charge $c = -4$ can be mapped to a Hermitian system with central charge $c = 2$. Lastly, we investigate the Galois conjugation in the Fibonacci model with the parameter $ϕ\to - 1/ϕ$, in which the transformation does not preserve both energy and entanglement spectra. We demonstrate the Fibonacci model and its Galois conjugation relate the tricritical Ising model/3-state Potts model and the Lee-Yang model with negative central charges from the scaling property of the entanglement entropy.
