论文标题
非手续拓扑（2+1） - 维相的纠缠光谱，具有强烈的时间逆转，锂甲烷态计数和PEPS
Entanglement spectra of non-chiral topological (2+1)-dimensional phases with strong time-reversal breaking, Li-Haldane state counting, and PEPS
论文作者
论文摘要
李 - 甲烷的对应关系[PRL 101，010504（2008）]通常用于帮助识别（2+1）-D手性拓扑阶段（即具有非零性手性中央电荷）的波功能，通过研究低裂解纠缠谱（ES）的长度圆周上的长圆柱。在这里，我们考虑了这种状态（实际上，某些投影纠缠的对状态（PEPS）]不是手性的（即具有零性手性中心电荷），但强烈打破了时间逆转和反射对称性，同时保留其产品，与呼射状态相同的对称性。这导致ES具有右手和左动力的分支，但速度却大不相同。对于周向比纠缠差距量表小得多，在某些拓扑部门中，低洼的ES在某些拓扑部门中出现手性，并且精确地遵循了真正手性阶段的李 - 雄性状态计数。这可能会导致人们将阶段误认为是手性。但是，考虑到所有部门的ES，可以观察到与手性阶段的明显差异。我们在Kurečić等人研究的$ SU（3）$ SU（3）$ Spin Liquid Peps中探讨了这一点。 [PRB 99，045116（2019）]，其中拓扑琐碎的部门具有手性$ su（3）$ level-One [$ su（3）_1 _1 $]的状态计数。实际上，PEPS具有$ d（\ Mathbb {z} _3）$拓扑顺序，带有9个扇区。我们计算与这些部门相对应的最小纠缠状态的ES，这些状态映射到9种Anyon类型的$ SU（3）_1 $ Chern-Simons拓扑场理论。 ES的状态计算与我们的期望相吻合：ES包含全球$ SU（3）$对称性的反对称性，来自（最低）的（最低）的“高速度” chiral $ su（3）_1 $ cft的原始状态（最低）的无用状态，与“低效率”的全部内容，均为“低级” chiral $ sucter a n of the Chiral $ su（3）$ cfft s y-cfft s cft s cft s cft s cfft s cfft s cfft s cfft在ES的拓扑琐事部门中。
The Li-Haldane correspondence [PRL 101, 010504 (2008)] is often used to help identify wave functions of (2+1)-D chiral topological phases (i.e., with non-zero chiral central charge) by studying low-lying entanglement spectra (ES) on long cylinders of finite circumference. Here we consider such ES of states [in fact, certain Projected Entangled Pair States (PEPS)] that are not chiral (i.e., having zero chiral central charge), but which strongly break time-reversal as well as reflection symmetry, while preserving their product, the same symmetry as a chiral state. This leads to ES with branches of both right- and left-moving chiralities, but with vastly different velocities. For circumferences much smaller than the inverse entanglement gap scale, the low-lying ES appear chiral in some topological sectors, and precisely follow the Li-Haldane state counting of a truly chiral phase. This could lead one to misidentify the phase as chiral. However, considering the ES in all sectors, one can observe distinct differences from a chiral phase. We explore this in an $SU(3)$ spin liquid PEPS studied by Kurečić, et al. [PRB 99, 045116 (2019)], where the topologically trivial sector has the state counting of a chiral $SU(3)$-level-one [$SU(3)_1$] Conformal Field Theory (CFT). In fact, the PEPS has $D(\mathbb{Z}_3)$ topological order, with 9 sectors. We compute the ES in minimally entangled states corresponding to these sectors, which map to the 9 anyon types of doubled $SU(3)_1$ Chern-Simons Topological Field Theory. The state countings of the ES coincide with our expectation: the ES contain irreps of global $SU(3)$ symmetry from the tensor products of the (lowest-lying) irrep of primary states of a "high-velocity" chiral $SU(3)_1$ CFT with the full content of a "low-velocity" chiral $SU(3)_1$ CFT sector, a non-chiral structure beyond that observable in the topologically trivial sector of the ES.
