提取圆环和柱面光谱信息的有效MPS方法
Efficient MPS methods for extracting spectral information on rings and cylinders
摘要：
基于MPS形式，我们引入了一种在开边界条件下捕获有限系统中的激发态的方法，为计算，例如，量子自旋链的光谱间隙这种方法可以直接在现有的DMRG或MPS基态代码之上实现。虽然这种方法是建立在开边界MPS，我们也将其应用到系统的周期性边界条件。尽管明确打破平移对称性的MPS表示，我们表明，动量出现作为一个很好的量子数，并可以利用标记的MPS基态上的激发。我们将我们的方法应用于环上的临界伊辛链和圆柱上的经典Potts模型。最后，我们应用同样的思想计算无限长圆柱上二维量子系统的激发谱。同样，尽管在周期方向上平移对称性明显破缺，我们仍将动量恢复为标记激发的良好量子数。我们将这种方法应用于2-D横场伊辛模型和半填充哈伯德模型;对于后者，我们获得了精确的结果，例如，圆柱体圆周的孔分散度可达八个位置。
英文摘要：
Based on the MPS formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can be straightforwardly implemented on top of an existing DMRG or MPS ground-state code. Although this approach is built on open-boundary MPS, we also apply it to systems with periodic boundary conditions. Despite the explicit breaking of translation symmetry by the MPS representation, we show that momentum emerges as a good quantum number, and can be exploited for labeling excitations on top of MPS ground states. We apply our method to the critical Ising chain on a ring and the classical Potts model on a cylinder. Finally, we apply the same idea to compute excitation spectra for 2-D quantum systems on infinite cylinders. Again, despite the explicit breaking of translation symmetry in the periodic direction, we recover momentum as a good quantum number for labeling excitations. We apply this method to the 2-D transverse-field Ising model and the half-filled Hubbard model; for the latter, we obtain accurate results for, e.g., the hole dispersion for cylinder circumferences up to eight sites.
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