发表机构
Indiana University; Harvard University; Instituto de Ciencia de Materiales de Madrid (CSIC); University of Kentucky（印第安纳大学; 哈佛大学; 马德里材料科学研究所（CSIC）; 肯塔基大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过解析与数值方法，发现腔真空涨落可在填充因子为1的量子霍尔铁磁体中驱动连续相变，形成以核心大小为序参量的紧凑核心相，光子数可作为实验探测信号。
AI 中文摘要
我们揭示了在填充因子 $\ u=1$ 的量子霍尔铁磁体（QHF）中，由腔的真空涨落驱动的一个连续相变。我们的分析从偶极规范下的朗道能级投影开始，发现该态可以很好地表示为电子和光子自由度的张量积。通过解析自旋波计算、平均场理论和密度矩阵重正化群（DMRG）模拟，我们表明对于空间反对称的腔场，均匀的QHF态仅在弱光-物质耦合下稳定，并在超过临界耦合时让位于电子密度不均匀的态。这些态涉及均匀QHF流体的“侧翼”，被一个双占据轨道的“紧凑核心”分隔，核心大小作为序参量，我们将其称为“紧凑核心相”。虽然完全自旋极化的电子态是乘积态，但在 $S_z=0$ 的磁扇区中，均匀QHF侧翼之间通过紧凑核心建立起纠缠，这为紧凑核心电子态提供了一个拟设。对于乘积电子态，相变边界以物质和腔参数精确推导得出，并通过DMRG数值确认。我们还研究了临界点附近的薄圆柱极限，其中量子涨落增强，以及通过纠缠谱简并性研究两相中的多体激发态。值得注意的是，发现光子数可以探测相变的序参量，为电子相变和紧凑核心态提供了可能的实验特征。我们的研究提供了一个罕见的例子，即仅通过与腔模增强真空涨落的耦合来稳定电子相。
英文摘要
We uncover a continuous phase transition in a quantum Hall ferromagnet (QHF) at filling factor $ν=1$, driven by vacuum fluctuations of a cavity. Our analysis starts with a Landau level projection in dipole gauge, where we find the states to be well-represented by a tensor product of the electronic and photonic degrees of freedom. Through analytic spin wave calculations, mean-field theory and density matrix renormalization group (DMRG) simulations, we show that for a spatially antisymmetric cavity field, the uniform QHF state is stable only for weak light-matter coupling and gives way to states of inhomogeneous electron density above a critical coupling. These states involve "flanks" of uniform QHF fluids, separated by a "compact core" of doubly occupied orbitals with the core size being the order parameter, which we dub as "compact-core phases". While the fully spin polarized electronic states are product states, entanglement builds up between the uniform QHF flanks across the compact core in the $S_z=0$ magnetic sector, motivating an ansatz for the compact-core electronic states. The transition boundary is exactly derived for product electronic states in terms of matter and cavity parameters, and numerically confirmed by DMRG. We also study the thin-cylinder limit near the critical point where quantum fluctuations are enhanced, and the many-body excited states in both phases by focusing on the entanglement spectrum degeneracies. Remarkably, the photon number is found to probe the order parameter of the transition, providing a possible experimental signature of the electronic transition and the compact-core states. Our study offers a rare example of a phase of electrons stabilized solely by coupling to the enhanced vacuum fluctuations of a cavity mode.
Comments34 pages, 13 figures
