Simulating superconductivity in mixed-dimensional $t_\parallel$-${J}_\parallel$-${J}_\perp$ bilayers with neural quantum states
Ludwig-Maximilians-Universität München（慕尼黑大学）；Max-Planck-Institute for Quantum Optics（马普量子光学研究所）；California Institute of Technology（加州理工学院）；Flatiron Institute（平顿研究所）；Collège de France（法兰西公学院）；Université PSL（巴黎文理研究大学）；Ecole Polytechnique, CNRS, Institut Polytechnique de Paris（巴黎综合理工学院，法国国家科学研究中心，巴黎理工学院）；Université de Genève（日内瓦大学）
Hannah Lange, Ao Chen, Antoine Georges, Fabian Grusdt, Annabelle Bohrdt, Christopher Roth
Motivated by the recent discovery of superconductivity in the bilayer nickelate La$_3$Ni$_2$O$_7$ (LNO) under pressure, we study a mixed-dimensional (mixD) bilayer $t_\parallel$-$J_\parallel$-$J_\perp$ model, which has been proposed as an effective low-energy description of LNO. Using neural quantum states (NQS), and in particular Gutzwiller-projected Hidden Fermion Pfaffian State, we access the ground-state properties on large lattices up to $8\times 8\times 2$ sites. We show that this model exhibits superconductivity across a wide range of dopings and couplings, and analyze the pairing behavior in detail. We identify a crossover from tightly bound, Bose-Einstein-condensed interlayer pairs at strong interlayer exchange to more spatially extended Bardeen-Cooper-Schrieffer-like pairs as the interlayer exchange is decreased. Furthermore, upon tuning the intralayer exchange, we observe a sharp transition from interlayer $s$-wave pairing to intralayer $d$-wave pairing, consistent with a first-order change in the pairing symmetry. We verify that our simulations are accurate by comparing with matrix product state simulations on coupled ladders. Our results represent the first simulation of a fermionic multi-orbital system with NQS, and provide the first evidence for superconductivity in two-dimensonal bilayers using high-precision numerics. These findings provide insight into superconductivity in bilayer nickelates and cold atom quantum simulation platforms.
Transverse Magnetic Susceptibility of a Frustrated Spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg Antiferromagnet on a Bilayer Honeycomb Lattice
Out-of-plane bond-order phase, superconductivity, and their competition in the $t$-$J_\parallel$-$J_\perp$ model: Possible implications for bilayer nickelates
Competing Interlayer Loop Currents and Superconductivity in the Bilayer $t$-$J_\perp$-$V$ Model
Facultad de Ciencias Exactas, Ingeniería y Agrimensura（理学院、工程学院和测量学院）；Instituto de Física Rosario (UNR-CONICET)（罗萨里奥物理研究所（UNR-CONICET））；Department of Physics, Nagoya University（名古屋大学物理学系）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
Collinear antiferromagnetic phases of a frustrated spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ Heisenberg model on an $AA$-stacked bilayer honeycomb lattice
Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model
Density-wave phases of dipolar fermions in a bilayer
我们研究了偶极费米子在二维双层膜中的相位图。利用最近适用于单层偶极费米子的Singwi-Tosi-Land-Sjolander方案[M. M. Parish和F. M. Marchetti，Phys. Rev. Lett. 108，145304（2012）]，我们在线性响应理论内确定双层系统的密度波不稳定性。我们发现，双层的几何形状可以稳定的崩溃的二维偶极费米气体层内吸引力，形成一个新的密度波相，具有垂直于密度波预期强层内排斥的取向。因此，我们得到的条纹相位之间的量子相变是由强关联和低维系统的架构之间的相互作用驱动的。
Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model
Ground state properties, excitation spectra and phase transitions in the $S=1/2$ and $S=3/2$ bilayer Heisenberg models on the honeycomb Lattice
受$S=3/2$材料Bi $_3$ Mn $_4$ O $_{12}$ NO $_3$中无序自旋基态观察的启发，我们研究了蜂窝晶格上的$S=3/2$（和作为比较的$S=1/2$）双层海森堡模型的基态性质和激发光谱，有和没有进一步的邻居相互作用。我们使用Néel态附近的级数展开来计算磁有序相的性质。此外，在$1/λ=J_1/J_{\perp}$，其中$J_1$是一个平面内的交换常数和$J_\perp$是层之间的交换常数的级数展开被用来研究自旋单线态相的性质。对于未受挫折的情况下，我们的相变的结果是在最近的量子蒙特卡罗研究非常好的协议。我们还获得了在无序相的激发光谱和研究的变化时，令人沮丧的交换相互作用添加到$S=3/2$系统中的关键$λ$，并找到一个快速抑制的有序相挫折。讨论了材料Bi $_3$ Mn $_4$ O $_{12}$ NO $_3$的含义。
