使用块Lanczos方法直接求解矩阵积态中的多重激发态
Direct solution of multiple excitations in a matrix product state with block Lanczos
AI总结：
本文提出多目标密度矩阵重整化群方法，作用于捆绑的矩阵积态，利用块Lanczos算法同时变分优化多个激发态，在Heisenberg模型等案例中验证了能在小键维度下高效可靠地获取大量激发态及局部可观测量。
摘要：
矩阵积态方法已知在计算局部、有能隙的哈密顿量的基态时十分高效，尤其在一维情况下。我们引入了多目标密度矩阵重整化群方法，该方法作用于一个捆绑的矩阵积态，包含多个激发态。使用块或带状Lanczos算法允许对激发态捆绑包进行同时的、变分的优化。该方法在Heisenberg模型和其他感兴趣的情况下得到了验证。可以在小的键维度下获得大量激发态，且在整个链上具有高度可靠的局部可观测量。
英文摘要：
Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted density matrix renormalization group method that acts on a bundled matrix product state, holding many excitations. The use of a block or banded Lanczos algorithm allows for the simultaneous, variational optimization of the bundle of excitations. The method is demonstrated on a Heisenberg model and other cases of interest. A large of number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain.
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