标题： 加权重归一化时间演化块消减用于改进量子动力学模拟 显示英文标题

标题： Reweighted Time-Evolving Block Decimation for Improved Quantum Dynamics Simulations

摘要： 我们引入了一种简单但重要的改进，用于模拟强关联一维（1D）混合量子态的时间动力学的时变块消去（TEBD）张量网络算法。 1D 张量网络方法的效率来自于使用矩阵的乘积来表示：波函数的系数，得到矩阵乘积态（MPS）；或者密度矩阵的期望值，得到矩阵乘积密度算子（MPDO）。 为了避免指数级的计算成本，TEBD 在模拟时间演化时会截断矩阵维度。 然而，当截断 MPDO 时，TEBD 并不会优先考虑低权重期望值，如$\langle c_i^\dagger c_j \rangle$，而不是指数级的高权重期望值，如权重为$n$的$\langle c_{i_1}^\dagger c^\dagger_{i_2} \cdots c_{i_n} \rangle$，尽管低权重期望值至关重要。 受此缺点的启发，我们提出了一种加权的 TEBD（rTEBD）算法，在截断过程中通过因子$\gamma^{-n}$来降低高权重期望值的优先级。 这种简单的修改（只需在 MPDO 中对某些矩阵按因子$\gamma$进行加权）使 rTEBD 比 TEBD 对 MPDO 的时间依赖模拟显著更准确，并且与使用 MPS 的 TEBD 相比具有竞争力，有时甚至更好。 此外，通过优先考虑低权重期望值，rTEBD 能够以高精度保持守恒量。 显示英文摘要

摘要： We introduce a simple yet significant improvement to the time-evolving block decimation (TEBD) tensor network algorithm for simulating the time dynamics of strongly correlated one-dimensional (1D) mixed quantum states. The efficiency of 1D tensor network methods stems from using a product of matrices to express either: the coefficients of a wavefunction, yielding a matrix product state (MPS); or the expectation values of a density matrix, yielding a matrix product density operator (MPDO). To avoid exponential computational costs, TEBD truncates the matrix dimension while simulating the time evolution. However, when truncating a MPDO, TEBD does not favor the likely more important low-weight expectation values, such as $\langle c_i^\dagger c_j \rangle$, over the exponentially many high-weight expectation values, such as $\langle c_{i_1}^\dagger c^\dagger_{i_2} \cdots c_{i_n} \rangle$ of weight $n$, despite the critical importance of the low-weight expectation values. Motivated by this shortcoming, we propose a reweighted TEBD (rTEBD) algorithm that deprioritizes high-weight expectation values by a factor of $\gamma^{-n}$ during the truncation. This simple modification (which only requires reweighting certain matrices by a factor of $\gamma$ in the MPDO) makes rTEBD significantly more accurate than the TEBD time-dependent simulation of an MPDO, and competive with and sometimes better than TEBD using MPS. Furthermore, by prioritizing low-weight expectation values, rTEBD preserves conserved quantities to high precision.