[论文解读] Evolution of entanglement entropy at SU($N$) deconfined quantum critical points

Menghan Song, Jiarui Zhao+5 more|arXiv (Cornell University)|Jul 5, 2023

Quantum Mechanics and Applications被引用 11

一句话总结

本文使用渐进式量子蒙特卡罗方法研究SU(N)去耦合量子临界点在N=2到N=20之间的纠缠熵，发现存在单位性共形不变点的有限临界N_c，且对于N≥7呈单位性共形场；N≤6呈非单位性行为，解释了SU(2)的伪临界性。

ABSTRACT

Over the past two decades, the enigma of the deconfined quantum critical point (DQCP) has attracted broad attention across the condensed matter, quantum field theory, and high-energy physics communities, as it is expected to offer a new paradigm in theory, experiment, and numerical simulations that goes beyond the Landau-Ginzburg-Wilson framework of symmetry breaking and phase transitions. However, the nature of DQCP has been controversial. For instance, in the square-lattice spin-1/2 $J$-$Q$ model, believed to realize the DQCP between Néel and valence bond solid states, conflicting results, such as first-order versus continuous transition, and critical exponents incompatible with conformal bootstrap bounds, have been reported. The enigma of DQCP is exemplified in its anomalous logarithmic subleading contribution in its entanglement entropy (EE), which was discussed in recent studies. In the current work, we demonstrate that similar anomalous logarithmic behavior persists in a class of models analogous to the DQCP. We systematically study the quantum EE of square-lattice SU($N$) DQCP spin models. Based on large-scale quantum Monte Carlo computation of the EE, we show that for a series of $N$ smaller than a critical value, the anomalous logarithmic behavior always exists in the EE, which implies that the previously determined DQCPs in these models do not belong to conformal fixed points. In contrast, when $N\ge N_c$ with a finite $N_c$ that we evaluate to lie between $7$ and $8$, the DQCPs are consistent with conformal fixed points that can be understood within the Abelian Higgs field theory with $N$ complex components.

研究动机与目标

• 研究SU(N) J1–J2–Q自旋模型在其去耦合量子临界点是否在各N下实现单位性共形不变点。
• 确定纠缠熵尺度如何反映单位性CFT描述的存在与否。
• 识别将连续的DQCP与弱一级行为分隔开的有限临界“味道数”N_c。

提出的方法

• 使用针对SU(N)自旋模型的渐增式QMC算法计算二阶Rényi纠缠熵S_A^(2)。
• 通过S_A^(2)(l)=a l − s ln l + c分析角落诱导的普适对数项s，其中l为边界长度。
• 将系统分割，包含四个90度角，以提取s及其符号。
• 比较不同N下的s(N)，评估是否与单位性CFT兼容（要求s≥0）。
• 将大N极限与Abelian Higgs和CP^{N−1}场理论联系起来，并用1/N展开形式拟合s(N)。

实验结果

研究问题

• RQ1 SU(N) DQCPs 的纠缠熵尺度是否指示不同N下的单位性CFT行为？
• RQ2 在何临界味数N_c之上，DQCPs与单位性共形不变点相符合？
• RQ3 s(N)的符号与大小如何随N演化，这对Miransky型伪临界性意味着什么？
• RQ4 大型N场论预期（Abelian Higgs / CP^{N−1}）是否与数值纠缠结果一致？

主要发现

• 对于N≤6，EE尺度给出的对数系数s为负，与单位性CFT不兼容，指示非单位性或非共形临界行为。
• 对于N≥7，对数系数s为非负，允许单位性CFT描述，指示真实的DQCP。
• 有限尺寸尺度和四环RG洞见与存在稳定临界不变点的N_c有限且≥7的结论一致，描述连续相变。
• 在大N极限，结果与Abelian Higgs / CP^{N−1}预测一致，支持存在有限的N_c，在N≥N_c时不变点碰撞导致单位性临界性。
• SU(2)情形（N=2）可通过不变点碰撞与湮灭解释，产生伪临界行为而非真正的DQCP。
• leading corner贡献s(N)符合预期的大N形式，近似s≈0.042(9)，支持在转变过程中的普适纠缠结构。