By considering an onsite attraction between a spin-$\uparrow$ and a spin-$\downarrow$ fermion in a multiband tight-binding lattice, here we study the two-body spectrum, and derive an exact relation between the inverse of the effective-mass tensor of the lowest bound states and the quantum-metric tensor of the underlying Bloch states. In addition to the intraband (or the so-called conventional) contribution that depends only on the single-particle spectrum and the interband (or the so-called geometric) contribution that is controlled by the quantum metric, our generalized relation has an additional interband contribution that depends on the so-called band-resolved quantum metric. All of our analytical expressions are applicable to those multiband lattices that simultaneously exhibit time-reversal symmetry and fulfill the condition on spatially-uniform pairing. As a nontrivial illustration we analyze the two-body problem in a Kagome lattice with nearest-neighbor hoppings, and show that the exact relation provides a perfect benchmark.
Simulation of many body localization and time crystals in two dimensions with the neighborhood tensor update
研究了无限正方晶格上具有离散无序的海森堡反铁磁体从初始Néel态随时间的演化.模拟是用邻域张量更新（NTU）算法对无限投射纠缠对态（iPEPS）进行的[Phys. Rev. B 104，094411（2021）]。辅助自旋用于对无序的$2$或$5$离散值求平均。随着键的尺寸达到$20$，演化时间足够长，以确定一个足够强的无序多体局域化制度。此外，相同的哈密顿量受到周期性自旋翻转的影响。对Floquet动力学的模拟表明，它可以维持足够强的无序的时间结晶阶段。
