论文标题
远程XXZ链的纠缠光谱和量子相图
Entanglement spectrum and quantum phase diagram of the long-range XXZ chain
论文作者
论文摘要
纠缠是多体量子系统的核心特征，在量子相变中起着独特的作用。 在许多情况下，代表双方系统密度矩阵的光谱的纠缠光谱包含唯一纠缠熵以外的有价值的信息。 在这里，我们研究了远程XXZ模型的纠缠光谱。我们表明，在关键阶段，它表现出了非凡的自相似性。 自相似性和从Luttinger液体的过渡与重新归一化的群体理论一致。 结合两者，我们能够确定模型的量子相图并找到相应的相变。我们的结果通过使用张量 - 网络技术的数值脱颖而出的计算证实。 此外，我们表明自相似重新恢复延伸至临界阶段中的几何纠缠以及Luttinger参数。 我们的结果为在远程量子模型中进一步研究纠缠特性铺平了道路。
Entanglement is a central feature of many-body quantum systems and plays a unique role in quantum phase transitions. In many cases, the entanglement spectrum, which represents the spectrum of the density matrix of a bipartite system, contains valuable information beyond the sole entanglement entropy. Here we investigate the entanglement spectrum of the long-range XXZ model. We show that within the critical phase it exhibits a remarkable self-similarity. The breakdown of self-similarity and the transition away from a Luttinger liquid is consistent with renormalization group theory. Combining the two, we are able to determine the quantum phase diagram of the model and locate the corresponding phase transitions. Our results are confirmed by numerically-exact calculations using tensor-network techniques. Moreover, we show that the self-similar rescaling extends to the geometrical entanglement as well as the Luttinger parameter in the critical phase. Our results pave the way to further studies of entanglement properties in long-range quantum models.
