论文标题
在二维中对本素态拓扑顺序的多体裂线化保护
Many-body-localization protection of eigenstate topological order in two dimensions
论文作者
论文摘要
已经提出了多体定位（MBL），以实现和保护所有本征态的拓扑秩序，从而大大扩展了传统的地面环境。但是，对于具有任何人和拓扑依赖性的二维（2D）系统的最有趣的情况，密集的多体频谱挑战在数值上研究了该MBL保护。在这里，我们使用大规模的全光谱变量Ansätze来证明受磁场扰动的无序的2D复曲面代码中受MBL保护的拓扑顺序。我们表明，该系统具有低于$ H_C \ $ H_C \大约0.1 $乘以复曲率代码耦合量表的磁场强度的拓扑局部运动积分（TLIOMS）。将tlioms与精确的对角线化结合，我们还确定了密集多体谱中的高能拓扑多重组。我们发现的相图与曲折的代码和琐碎的MBL相通过中间热相分开。
Many-body localization (MBL) has been proposed to enable and protect topological order in all eigenstates, vastly expanding the traditional ground-state setting. However, for the most intriguing case of two-dimensional (2D) systems with anyons and topology-dependent degeneracies, the dense many-body spectrum challenges studying this MBL protection numerically. Here we use large-scale full-spectrum variational ansätze to demonstrate MBL-protected topological order in the disordered 2D toric code perturbed by magnetic fields. We show that the system has topological local integrals of motion (tLIOMs) for magnetic field strengths below $h_c\approx0.1$ times the toric code coupling scale. Combining tLIOMs with exact diagonalization, we also identify high-energy topological multiplets in the dense many-body spectrum. The phase diagram we find is consistent with toric-code and trivial MBL phases being separated by an intervening thermal phase.
